0）内的一个定点,四边形DEPF为矩形,点E、F在圆上,M为对角线的交点（1）求动点P的轨迹方程（2）当r=5,a=1,且OM取最小值时,求E,F的坐标">
D（a,0）是定圆O:x²+y²=r²（r>0）内的一个定点,四边形DEPF为矩形,点E、F在圆上,M为对角线的交点（1）求动点P的轨迹方程（2）当r=5,a=1,且OM取最小值时,求E,F的坐标_百度作业帮
D（a,0）是定圆O:x²+y²=r²（r>0）内的一个定点,四边形DEPF为矩形,点E、F在圆上,M为对角线的交点（1）求动点P的轨迹方程（2）当r=5,a=1,且OM取最小值时,求E,F的坐标
D（a,0）是定圆O:x²+y²=r²（r>0）内的一个定点,四边形DEPF为矩形,点E、F在圆上,M为对角线的交点（1）求动点P的轨迹方程（2）当r=5,a=1,且OM取最小值时,求E,F的坐标R.o.x.y.p.o.l.e.d.a.n.c.e.r | Pole.Run.Eat.Recipes.Travel
Gluten-free Granola
I love granola for some reason even though I know it’s not that all healthy. I love having granola with greek yogurt or just eat it on its own as teatime snack. Since it has to be gluten-free, I used Bob’s Red Mills gluten-free rolled oats. Raided the fridge and found: a pack of dried blueberries in the fridge (which were super sweet), leftover bitter chocolate Valrhona chocolate bits, walnuts and chia seeds. Mixed them in a mixer bowl with Grade 2 Canadian maple syrup and honey, toasted the mix in a frying pan and then put in a preheated oven at 200 deg c for 15 mins. Easy.
Shepherd’s Pie
This is a dish that I pride myself in making as it is the first dish I learnt to make in my teenage days and had made it so many times I think I’ve mastered it. It was my friend Cassandra’s mom who taught us how to make it when I went for a sleepover. I was surprised at how easy it was to make this awesome party food.
Cassandra’s mom’s recipe used tomato puree which I think is the English style pie. Gordon Ramsay uses tomato puree too. Nothing wrong with that. For this recipe, I didn’t wanted my minced beef to be very wet so I didn’t use tomato puree. Here’s my recipe.
INGREDIENTS
200g minced beef
1 bowl mixed vegetables (carrots, corn and peas)
Fish sauce
Brown sugar
Dried basil
Oyster sauce
Shredded cheddar or mozzarella
I packet of washed potatoes
INSTRUCTIONS
Marinate the beef with fish sauce, salt, sugar, garlic, oyster sauce, basil and oregano (you can use your favourite herbs). Leave the marinated beef in the fridge for a few hours.
In the meantime, boil unpeeled potatoes for 45 mins. After potatoes are cooked, peel and mash. Add butter, egg, salt and pepper to taste.
Heat the oven at 200 deg c. Cook the beef in frying pan. Once it’s cooked, scoop the beef into a casserole dish place the mashed potato on top of the beef. Top with cheddar or mozzarella cheese. Bake in the oven for about 15 mins or when the cheese turns light brown.
After a hiatus of almost more than six months, I felt inspired to make my own bento for lunch. I don’t have pictures of each step but I’ll try and see if I can explain it clearly here.
Sleeping Rilakkuma bento
Rilakkuma Bento
INGREDIENTS
1 cup Japanese rice
1 slice American cheese (I use Kraft)
1 tbsp white vinegar or apple cider vinegar (which I usually use)
2 pieces of Konbu (kelp)
1 tbsp soy sauce
1 tbsp sugar
1 tsp salt
INSTRUCTIONS
Soak rice in water for 30 minutes. Drain water. Cook rice in fresh water, add vinegar, some salt and sugar. I also added one piece of konbu. How I measure the amount of water to put in is to place my hand onto the rice and the water should just cover 3/4 of your hand. Cook rice in rice cooker for about 10 mins. Leave rice in cooker for a few minutes for the water to dry out. I let the rice cool for a bit before transferring to a pan to fry the rice with garlic and ketchup, add a pinch of salt. When the rice is cooled, roll rice using glad wrap. Roll rice for Rilakkuma’s head, body, two hands and two ears.
To cook the egg, firstly I boil konbu in some water (just a little bit, maybe 1/2 cup), add some sugar and soy sauce. Cook for about 2 mins. Let it sit for a few minutes. I use a Japanese rectangle non-stick pan to fry the egg, pouring in a thin layer for Rilakkuma’s ‘blanket’ and a bit thicker for his “pillow”.
Cut American cheese into shapes for Rilakkuma’s ears, hands and mouth/nose area. Cut seaweed into shapes for Rilakkuma’s sleeping eyes and nose. Lay out the egg pillow, head, body, hands and blanket. Then add the cheese, then seaweed. Garnish with your favourite meat or vegetables. I like to use carrots and parsley/cilantro.
Totoro Bento
Totoro Bento
INGREDIENTS
1 cup Japanese rice
1 slices American cheese (I use Kraft)
Black sesame seeds (I used chia seeds) to make Totoro grey in colour
1 tbsp white vinegar or apple cider vinegar (which I usually use)
2 pieces of Konbu (kelp)
1 tbsp soy sauce
1 tbsp sugar
1 tsp salt
INSTRUCTIONS
Making Totoro bento has got to be easier than Rilakkuma cos it has less body parts. Cook rice the same way. Mix rice with black sesame seeds (I used chia seed but it didn’t turn out grey as I wanted it to be).
Shape Totoro’s body (like a big egg) and ears. Cut cheese and seaweed for his eyes and stomach. Serve with eggs, meat (I like to use salmon), and your favourite vegetables.
Totoro bento
Totoro bento
This has got to be my favourite homemade gluten-free pizza ever. It’s so simple to make and it’s so yummy!
INGREDIENTS
1/2 cup quinoa (I used tri-coloured quinoa)
1/4 cup chia seeds
1/2 cup mozzarella
1 tsp baking powder
INSTRUCTIONS
Preheat oven at 220 deg c. Cook quinoa and chia seeds in chicken stock. Don’t put too much water as you want the water to dry out from cooking. Once quinoa is cooked and crispy, let it cool for about 10 minutes.
In a separate bowl, beat 2 eggs, mix in mozzarella, oregano, pepper, salt and baking powder. Add mixture to cooked quinoa. Lay baking sheet on tray. Spray cooking oil on baking sheet. Spread the quinoa mixture onto baking sheet. Top with mozzarella.
Matcha mushipan
I love steamed egg cake and haven’t had it for a long time since I went gluten-free. Today I decided to try matcha steamed egg cake for the first time using rice flour. You can also use almond flour or gluten-free flour.
Steam for 30 mins
INGREDIENTS
8 oz rice flour
8 oz castor sugar
1 1/2 tbsp matcha powder
1 tsp vanilla essence
Pinch of salt
1 tsp coconut oil
INSTRUCTIONS
Heat up steamer. Beat eggs and sugar until light and fluffy. Beat for about 15 mins. Note that this step is very important as it determines how light and fluffy your cake will turn out. So don’t try any short cuts. Add vanilla essence. Add sifted rice flour and matcha powder and a pinch of salt and mix. Pour mix into baking paper lined round tin. Sprinkle sugar across the batter into a cross. Lightly drop the tin on table to get rid of air bubbles. Steam for 30 minutes. Cool on cooling rack and it’s ready to be served with milk, tea or coffee!
Just out from the steamer
This is something I’ve never thought I’d ever make as I used to think that this is too troublesome to do. I was asking my friend what to do with the Valrhona dark chocolate I bought some months ago. She showed me Alton Brown’s “Good Eats” episode on truffles and verbally explained to me how to make it. Yesterday, I woke up and decided to make some Valrhona truffles.
INGREDIENTS
200g Valrhona 75% dark chocolate
2 tbsp Baileys irish cream
3 tbsp unsalted butter
1/2 cup thickened cream
1/2 cup Hersheys cocoa powder
1/2 cup dessicated coconut
DIRECTIONS
Boil thickened cream and butter in a stainless steel pot for a few minutes. Remove pot from stove and put in the dark chocolate. Stir chocolate in until it melts in the cream. Add irish cream. Place mixture in container and leave in fridge for an hour. After an hour, remove from fridge and use a measuring 1/2 tsp scoop (I use the scoop I bought from Ikea) to scoop chocolate and roll into a ball. As I didn’t have glove, I used my hands. I had to roll it fast as the chocolate melts fast in the hands. Roll chocolate ball into cocoa powder or coconut and leave it in for 20 seconds before taking out and placing into an airtight container. Surprisingly quite easy to make. Enjoy!
It was a friend who chanced upon a blog about an abandoned 19th century house in Singapore and made us all excited to visit this hidden gem that sits on prime land in the city. We searched the internet for more information and read various blogs on how to get to the house named “Woodneuk”. After getting a rough idea that the ‘entrance’ is right opposite Dempsey Road, my friends and I decided to visit this place one Sunday afternoon.
We walked along Holland Road and stared at the row of hideous vegetation that for years remained so mysterious to us. Who knew that there is a house in there? Even there and then, as we gazed into the greenery, we wondered if there is a house in there (maybe it was burnt down or the government bought over the land for developments?). We were not sure but since we were already on this mission to find the house, we decided to stick to the plan.
We found an obvious ‘hole’ amongst thick vegetation somewhere near the bus stop along Holland Road opposite Dempsey Road (just like what one blogger described). We looked around and when there was nobody walking along the foot path, we ‘sneaked’ in.
The forest was dark with tall trees and fallen branches everywhere. We climbed a rather steep and slippery soiled slope and ploughed through thick forest, feeling scared (of ghosts) and apprehensive (about finding the house). But those feelings didn’t last for long as to our surprise we saw the house as soon as we came out of the forest. It took us no more than five minutes to get there!
The house looked just like in the photos we saw on the internet. I could not stop exclaiming ‘Wow’ as we walked towards the house on a footpath. I just could not believe what I saw. It was a beautiful house and looked pretty much intact and in good condition considering it is more than a hundred years old.
The beautiful Woodneuk
Lush greenery
Surrounded by the lushness of untouched rainforest, Woodneuk sits on a 14-hectare land (equivalent to about 26 football fields) that is today, still owned by the Sultan of Johor. There was rich biodiversity as we saw birds, butterflies, and dragonflies. No snakes though! With Singapore Botanic Gardens and the upcoming Tyersall Learning Forest as neighbours, we wonder how long Woodneuk will remain in its peaceful surroundings
My favourite part of the house is the rusty Victorian iron railings used along stairways and balconies, which in my opinion, brings out a royal and classy character of the house that was tastefully designed in every detail.
I read online that Woodneuk was built by the 21st Sultan of Johor, Abu Bakar bin Daing Ibrahim (), for his fourth wife, Khadijah. The house was later sold to his son. It is not sure why the house was vacated but I’m guessing that they left when Singapore became independent from Malaysia.
The massive house took us some one hour to explore. There were two storeys. The second floor was pretty much open as it was roofless. Some of the walls / partitions were also gone / hacked away so we couldn’t really make out where the bedrooms were. There were big balconies surrounding the house for enjoying the greenery.
We saw graffiti on one of the walls and found a bathtub in one corner which I guessed must have been attached with the master bedroom. It was also where I got stung by two wasps on my face as I was busily snapping away on my camera.
The first level was dark. Luckily we brought our torch. There were many rooms (pantry, bathrooms, store room, etc). We also found burnt car doors, refrigerators, catering chairs and a narrow stairway that leads to the second floor. We made up stories on what events may have taken place in the house. The catering chairs and food racks we saw showed that the Sultan had organised many parties in the house.
It rained heavily when we left. The slopes became more slippery on the way out but we made it out! The house was not as eerie as I thought it would be. It was a Sunday afternoon well spent visiting a relatively unknown historic site. We found the guard house which was quite a distance from the house, and a small house beside Woodneuk which was likely the maids’ house, but were disappointed that we didn’t find the main entrance to the estate. Till next time. We will definitely visit Woodneuk again.
For those who love tom yum, this is the best I’ve ever had and it’s really fast and easy to make! The recipe is from Silom Cooking School which I took a class when I was in Thailand on Saturday.
INGREDIENTS
1 lemongrass cut into pieces
3 kaffir lime leaves torn in half
10 sliced galangal ginger
1/2 tablespoon fish sauce
1/4 tablespoon lime juice or lemon juice
1 cup water or chicken stock
1/2 tomato cut in quarter
1 tablespoon coriander leaves chopped
1 tablespoon green onions chopped
1/2 Thai chilli paste (nam prim pow)
2 tablespoon coconut milk or fresh milk
3 chillies
1/2 cup prawns
1 straw mushroom
INSTRUCTIONS
Fry lemongrass, galangal, kaffir lime leaves, mushrooms, chilies, and tomato. Add water and cook till tender. Add prawns. Add coconut milk, lime juice, fish sauce and Thai chilli paste. Garnish with fresh coriander and green onions.
Homemade corn tortilla haystacks
I love this gluten-free dish and it’s so easy to make! I’ve served this at parties and everyone loved it more than the chicken pie on the table (sorry Ken)! I also made for my friends in San Francisco (who love corn tortillas) and they really liked my homemade haystack. It’s wonder how come it’s not a common dish in America! Here’s my completely made-up recipe so I’m sorry I don’t have the portions. Just put as much as you like. I like to go with the flow:
INGREDIENTS
1 pack tortilla chips (I love ‘Mission’ brand)
1 can refried or me-xe beans
Red onions
4 cloves garlic
Taco mix or you can add cumin powder and chilli powder
Spinach or lettuce
2 avocados
2 tablespoons jalape?o
Shredded cheddar
Feta cheese
INSTRUCTIONS
For the cooking bit, all you need to do is to fry garlic and onion with refried or me-xe beans. Add chopped tomato at the end.
On a plate, assemble the spinach or lettuce, followed by tortilla chips. Pour in beans and sauce on top of chips. Add jalape?o and feta on the side and sprinkle cheddar on top of hot beans so it melts. Separately, I will mash the avocados and make a simple guacamole without onions and tomatoes. Add guacamole on side. I guarantee this dish is yummilicious.
Wuerstelstand @ Trengganu St (Chinatown)
I seem to be playing tourist whenever I’m out on a hunt for food. I guess it’s because I rarely go to hawker centres or find food at dodgy back alleys or quiet housing estates.
After pole practice at Pole Lab @ 31 Kreta Ayer Road today, I chanced upon this Austrian sausage stall in this coffee shop in Chinatown called Wuerstelstand. I love sausages so I was excited about this one. Besides, I knew about this sausage guy from watching a local food show on TV eons ago and I remembered trying his sausage at his makeshift stall at a Chinese New Year
in Chinatown (not far from his current permanent stall).
We ordered the meat loaf and frankfurter. They were simple, no frills and good for a quick snack (even though it was our dinner).
Frankfurter with mash and sauerkraut (SGD$6)
Meatloaf and mash with dried onions on top (SGD$6)
Little Vietnam Cafe @ 511 Guillemard Road
Located just at the intersection of Geylang Road and Guilemard Road, this Little Vietnam Cafe is bustling with sophisticated youth and working adults even on a rainy Tuesday evening. All wait staff were Vietnamese (girls) who don’t speak or understand much English.
Even though the dishes were numbered in the menu, I still had difficulty communicating with them as we were placing our orders.
I thought it would be straightforward to just tell them the number, but when I wanted to order no.44b in the menu, the waitress thought I wanted no.44 with ‘beef’. LOL.
Despite communication problems, the food was inexpensive and delicious (even better than my favourite Phoa Hoa @ Holland Village). We spent SGD$25 in total for three dishes and two coffees. I will come back again! And bring more friends! 
Viet salad (SGD$5)
For starter, we had chicken salad which came with cabbage, laksa leaves, basil. Was soooooo good.
Rice vermicelli with deep-fried spring roll and grilled pork (SGD$8)
For my main dish, I had rice vermicelli with grilled pork and deep – fried spring rolls. Totally gluten-free and sooooo delicious!
Stir-fried rice vermicelli (SGD$8)
Sstir-fried vermicelli (tastes like for fun). It was yummy too!
The way they serve their Vietnamese coffee is interesting and yet seems old skool. Coffee was really good too!
Dim Sum @ Blk 350 Clementi Ave 2
I’ve been patronising this dim sum stall in the coffee shop since 2006. Eight years later today, I visited the stall (with my friend, Adeline) and it’s still cheap and good. Each dish costs only about $2!
The way I usually order is just look at what they have on the table in the stall. It’s faster that way.
Just choose from here.
Here’s what the two of us had. Total bill came to just SGD$11.80!
Minced pork and prawn ball (SGD$2)
Har kow (SGD$2)
Bacon roll (SGD$2)
Fan choy (SGD$2)
Seaweed roll (SGD$2)
Latest Posts（2005●嘉兴）在坐标平面内，半径为R的⊙O与x轴交于点D（1，0）、E（5，0），与y轴的正半轴相切于点B．点A、B关于x轴对称，点P（a，0）在x的正半轴上运动，作直线AP，作EH⊥AP于H．
（1）求圆心C的坐标及半径R的值；
（2）△POA和△PHE随点P的运动而变化，若它们全等，求a的值；若给定a=6，试判定直线AP与⊙C的位置关系（要求说明理由）．
（1）由题意知圆心C点的横坐标为DE中点的坐标，纵坐标和B点纵坐标相等，用切割线定理求出OB的长即可，C点的横坐标等于半径；
（2）因为△POA≌△PHE，OE的长为直角边和斜边的和，而OE的长已求，用OP表示PE，并且OA=OB．
根据勾股定理求出OP的长即为a的值，过A作圆的切线为标准证明AP与⊙C的关系．
解：（1）连接BC，则BC⊥y轴．
取DE中点M，连CM，则CM⊥x轴．
∵OD=1，OE=5，
∵OB2=OD×OE=5，
∴OB=√5．
∴圆心C（3，√5），半径R=3．
（2）∵△POA≌△PHE，
∵OA=OB=√5，OE=5，OP=a，
∴PA2=a2+5，
PE2=（5-a）2，
∴a2+5=（a-5）2，
（3）解法一：
过点A作⊙C的切线AT（T为切点），交x正半轴于Q．
设Q（m，0），则QE=m-5，QD=m-1，
QT=QA-AT=QA-AB=√m2+5-2√5．
由OT2=QE×QD，
得（√m2+5-2√5）2=（m-5）（m-1），
2√5（m2+5）=3m+10，
11m2-60m=0．
∴m=6011&．
∵a=6，点P（6，0），在点Q（6011&，0）的右侧，
∴直线AP与⊙C相离．
设射线AP、BC交于点F，作CT⊥AF于T．
∵△AOP∽△CTF，
∴CTCF&=AOAP&．
而AO=√5，AP=√41，
CF=BF-BC=12-3=9，
∴CT9&=√5√41&，
CT=9√5√41&＞9√5√45&=3=R，
∴直线AP与⊙C相离．