Question

Need help on the following three problems.

http://prntscr.com/k2ax1
http://prntscr.com/k2zfr

Answer 1

Okay, first, are you familiar with completing the square? That's for the first.
Next, asymptote is \(y=\pm \frac{b}{a} x\)
Foci= when y=0

Answer 2

Do you need further help?

Answer 3

No I am not familiar with completing the square, I'm really lost on this whole section. Yes further help would be nice!

Answer 4

lol Well, for example, completing x^2 + ax + b is
x^2+ ax + (a/2)^2 -(a/2)^2+ b
=(x+a/2)^2 + b -(a/2)^2
note that the a is divided by two before the square is completed.

Answer 5

Is that what I do for the first one?

Answer 6

Yup! do that for x and y. Go slow though it's quite dangerous.

Answer 7

Could you walk me through the second one?

Answer 8

For the second one, it has a change of axes. So first thing we do is see which hyperbola has it axeschanged. Look for the hyperbola with x+6 and y-6

Answer 9

then, since the asymptotic gradient formula is \(m= \pm \frac{b}{a}\), we look for the hyperbola with b = 6 and a =11
you follow?

Answer 10

Well there are two choices that have x+6 and y-6 I want to say its my first choice because the first denominator is 36 and the second is 121

Answer 11

well, the first denominator is the a^2 and the second is b^2

Answer 12

so the second fraction should have 36 and first 121?

Answer 13

yup! :)

Answer 14

(x+6)^2/121 and (y-6)^2/36?

Answer 15

yh!

Answer 16

Now how would I go about this last one? http://prntscr.com/k2zfr

Answer 17

well, for this one, first, the foci is supposed to be (ae,0)

Answer 18

So, you'll need to find e first. Then, since there is a change of axes by (-10, -1) you'll need to add that to the foci you've found

Answer 19

Okay, I think I got that one could we go back to the first one I'm stuck on it haha.

Answer 20

\(16x^2 -64x -25y^2-50y-361=0\)
so, \(16(x^2 -4x) -25(y^2+2y)-361=0\)
\(16(x^2 -4x+(\frac{-4}{2})^2-(\frac{-4}{2})^2) -25(y^2+2y+(\frac{2}{2})^2-(\frac{2}{2})^2)-361=0\)

Answer 21

Is this too vague? lol

Answer 22

So lost, but I appreciate the work you put it haha

Answer 23

lol start from the second line. Complete the square in the brackets for x first lol

Answer 24

16x^2 -( -125)? 25y^2 + 50y? - 361 = 0?

Answer 25

Sorry if you think I'm stupid, math really isn't my strong point.

Answer 26

Lol sorry about sudden leave.
You'll have to arrange it until it looks like a uncompleted quadratic eq before you complete it.

Answer 27

I'm pretty sure I got them, I really appreciated the help and I will definitely be communicating with you again soon.

Answer 28

lol You're welcome :)