1. ## Conic Sections assistance

I would really appreciate your help, if anyone can give it. I'm so stuck.

I've got a worksheet due and I've got two problems that I'm stumped on.

1) Find the foci of a hyperbola with the equation 9y^2-72y-16x^2-64x-64=0

2) Find the slopes of the asymptotes of a hyperbola with the equation y^2=36+4x^2.

If you would, please explain your steps so I can understand what you're saying.

Much appreciated

2. Originally Posted by ScottStedman
...
1) Find the foci of a hyperbola with the equation 9y^2-72y-16x^2-64x-64=0

2) Find the slopes of the asymptotes of a hyperbola with the equation y^2=36+4x^2.

...
1. Re-write the equation of the hyperbola in standard form:
$
\begin{array}{l} 9y^2-72y-16x^2-64x-64=0 \\ \implies 9(y^2-8y+16)-16(x^2+4x+4)=64+144-64
\\ \implies \dfrac{(y-4)^2}{4^2} - \dfrac{(x+2)^2}{3^2}=1 \end{array}$

Now you know: The hyperbola is opening up.
M(-2, 4)
a = 4, b = 3
$e = \sqrt{a^2+b^2}$
$F_1(-2, 4+e)$ , $F_2(-2, 4-e)$

2. Re-write the equation in standard form. Determine the coordinates of M and the lengthes of the axes.
The slope of the asymptotes is $m_{1,2} = \pm \dfrac ba$
The asymptotes pass through M.