a^2= 5^2= 25

b^2=3^2=9

Vậy phương trình chính tắc của elip là:

x^2/25+y^2/9=1

–Thay a² và b² vào dạng tổng quát, phương trình chính tắc của elip là:
x²/25 + y²/9 = 1

MF21+MF22=12

Diện tích ∆ MF1MF2 =1

–MF1^2 + MF2^2 = 12
–Diện tích tam giác MF1F2 = 1

a: Tọa độ trung điểm I của AB là:

\(\begin{cases}x_{I}=\frac{x_{A}+x_{B}}{2}=\frac{1-2}{2}=-\frac12\\ y_{I}=\frac{y_{A}+y_{B}}{2}=\frac{2+3}{2}=\frac52\end{cases}\)

=>I(-0,5;2,5)

A(1;2); B(-2;3)

=>\(\overrightarrow{AB}=\left(-2-1;3-2\right)=\left(-3;1\right)\)

(d) là đường trung trực của AB

=>(d)⊥AB tại trung điểm I của AB

=>(d) nhận \(\overrightarrow{AB}=\left(-3;1\right)\) làm vecto pháp tuyến và đi qua I(-0,5;2;5)

Phương trình (d) là:

-3(x+0,5)+1(y-2,5)=0

=>-3x-1,5+y-2,5=0

=>-3x+y-4=0

b: (Δ1)//(Δ2)

=>(Δ1): x-y+c=0

Thay x=1 và y=2 vào (Δ1), ta được:

1-2+c=0

=>c-1=0

=>c=1

=>(Δ1): x-y+1=0

c: A(1;2); B(-2;3)

=>\(AB=\sqrt{\left(-2-1\right)^2+\left(3-2\right)^2}=\sqrt{3^2+1^2}=\sqrt{10}\)

Phương trình đường tròn (C) là:

\(\left(x-1\right)^2+\left(y-2\right)^2=AB^2=10\)

d:

x-y+3=0

=>y=x+3

M thuộc (Δ2) nên M(x;x+3)

M(x;x+3); A(1;2)

MA=2

=>\(MA^2=4\)

=>\(\left(x-1\right)^2+\left(x+3-2\right)^2=4\)

=>\(\left(x-1\right)^2+\left(x+1\right)^2=4\)

=>\(x^2-2x+1+x^2+2x+1=4\)

=>\(2x^2=2\)

=>\(x^2=1\)

=>\(\left[\begin{array}{l}x=1\\ x=-1\end{array}\right.\)

Khi x=1 thì M(1;4)

Khi x=-1 thì M(-1;2)

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Minh agree to pay for my ticket

282.She/me//later/ phone/ offered.

She offered to phone me later

283. had/yesterday/ dinner/ We/ 6 p.m.

We had dinner at 6 p.m yesterday

284. very/John/patient. He/ doing/keeps/ until/ things/ successful/ he

John is very patient. He keeps doing things until he is successful

285. English/today/I/ study/begin.

I begin studying English today

286. Da Lat/photo/is/ city/beautiful/ The.

The photo is the beautiful city Da Lat

287. Now/cartoons/watch/on/ she/TV/

Now she is watching cartoons on TV

288. get usually/you/ What time/ up?

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He could read when he was five

260. He/not have/rice/ the fridge.

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261. there/be/starfruits/basket.

There are some starfruits in the basket

262. he/ not believe/ghost.

He doesn't believe in ghost

263. yesterday morning/she/buy/present/her mother.

Yesterday mornings she bought a present for her mother

264. 1/do/homework/this morning.

I did my homework this morning

265, she/always/expect/win/ any games.

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266. my sister/avoid / walk alone/night.

My sister avoids walking alone at night

267. Kevin/read/newspaper / at the moment.

Kevin is reading newspaper at the moment

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Are you telling a story now?

269, what/you/do/when/1/call/ you / this morning/?

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270, his daughter/can/write/when/she/be/four.

His daughter could write when she was four

Bán kính hình B gấp 3 lần hình A thì chu vi hình B gấp 3 lần chu vi hình A

Do đó hình A lăn 3 lần xung quanh hình B để quay trở lại điểm xuất phát