Question

What are the foci of the ellipse given by the equation 4x2 + 9y2 – 32x + 18y + 37 = 0?

(4, –1 ±square root of 5)

(4, –1 ±square root of 13)

(4 ±square root of 5 , –1)

(4 ±square root of 5 , 1)

Answer 1

@satellite73

Answer 2

this is a pain in the neck
you have to make it look like
\[\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1\] by completing the square for both the \(x\) and\(y\) terms
any idea how to do that?

Answer 3

Yes

Answer 4

ok let me know what you get when it is in the form \[\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1\] and then we can answer the question

Answer 5

Oh no that I do not know.

Answer 6

well then you can't solve the problem!

Answer 7

i can walk you through it if you like

Answer 8

yes please

Answer 9

\[4x^2 + 9y^2 – 32x + 18y + 37 = 0\] group the terms together and get
\[4x^2-32x+9y^2+18y=-37\] then factor out the coefficient of the \(x^2\) and \(y^2\) terms go get
\[4(x^2-8x)+9(y^2+2y)=-37\] so far so good?

Answer 10

yes

Answer 11

ok good
what is half of 8 ?

Answer 12

4

Answer 13

so it is either a or b

Answer 14

hold on
what is \(4^2\)

Answer 15

16

Answer 16

ok and finally, what is \(4\times 16\)?

Answer 17

64

Answer 18

ok so now we can turn
\[4(x^2-8x)+9(y^2+2y)=-37\] in to
\[4(x-4)^2+9(y^2+2y)=-37+64=27\]

Answer 19

So is it B

Answer 20

now we have to repeat the process with the \(y\) terms
half of 2 is 1
1 squared is 1,
9 times 1 is 9

Answer 21

I think it is B right. /-\

Answer 22

\[4(x-4)^2+9(y^2+2y)=-37+64=27\] is now
\[4(x-4)^2+9(y+1)^2=27+9=36\]

Answer 23

now divide all by \(36\)

Answer 24

Oh so it is A

Answer 25

Sorry it is because I have been studying since 3PM until now.

Answer 26

you are guessing, and still not done for sure

Answer 27

you get
\[\frac{(x-4)^2}{9}+\frac{(y+1)^2}{4}=1\]

Answer 28

Oh so it is D now that I understand.

Answer 29

One more question please I am so tiered but I must complete this last question.

Answer 30

no, it is not D

Answer 31

Oh so what is it?I am so sorry again.

Answer 32

center is \((4,-1)\) right?

Answer 33

As I said before if it is not written in the question then it is not their.

Answer 34

and here \(a^2=9\) making \(a=3\), \(b^2=4\) making \(b=2\) and the focus is \(\sqrt{9-4}=\sqrt{5}\) units to the left and right of the center

Answer 35

So it is A as I said previously before.

Answer 36

lol no

Answer 37

you keep missing C
it is always C

Answer 38

\(\sqrt{5}\) units left of \((4,-1)\) is \((4-\sqrt{5},-1)\)

Answer 39

HA I always guess c but it has been failing me lately.

Answer 40

Thnx JUST ONE MORE AND I WILL STOP DISTRUBING YOU AND I WILL BE OUT OF YOUR LIFE FOR TODAY

Answer 41

it is a lot of work
okay

Answer 42

Also why can I not message you.

Answer 43

because i have that annoying feature turned off

Answer 44

Oh so can I message you or will I be annoying.

Answer 45

no one can

Answer 46

I posted the new question. Also ok thanx. Well except for the people that you fanned.