Question

Graph 4x^2-9y^2+8x+36y-68=0
Find the center and name the curve, find the vertices, foci and asymptotes. Please sombody help me solve this whole problem

Answer 1

You can tell already that it's not a circle (by the question of course) but also because the coefficients in front of the highest exponent are not equal,
so to get the additional informations you want to use completing the square for x and y.

Answer 2

?

Answer 3

do you know what completing the square is?

Answer 4

Yes but I need help with this whole problem

Answer 5

well that's your first step then (-:

Answer 6

then after?

Answer 7

get it in this form

\[ \Large \frac{x^2}{a^2}-\frac{y^2}{b^2}=1 \]

Answer 8

there you have a lot of informations already, I assume it's going to be a hyperbola, because of the minus sign.

Answer 9

I dont no how do do this stuff I need an example bits and pieces are only confusing me

Answer 10

\[ x^2 +2x =0 \]
Completing the square gives you

\[ x^2+2x+1=1 \\(x+1)^2=1\]

Answer 11

I know how to complete the square thats about all i can do the rest I dont get

Answer 12

Well, if you have done completing the square, write down your result here and we can continue.