Thread: confusing math on conics

Given (y-2)^2 - X^2/4=1, do the following

a) write the equation in general form:

my answer:
(y-2)^2 - X^2/4=4
4(y-2)^2-1(x)^2=4
4(y^2-4y+4) -1(x^2+x)=4
4y^2-16y+16-(x^2+x)= 4
4y^2-16y+16-X^2+x=4
-x^2+4y^2+x-16y-16=4
-x^2+4y^2+x-16y-20=0

general form:
-x^2+4y^2+x-16y-20=0

How do I locate the vertices and center of this hyperbola??
thanks for your help!!!

Hello, Justin!

Given: .

1) Find the center and vertices of the hyperbola.

I must ask: Do you know anything about the hyperbola?

We have: .

The center is: . .

The hyperbola is "vertical":

The vertices are one unit above and one unit below the center.
. .

2) Write the equation in general form

Your algebra is faulty . . .

We have: .

Multiply by

. .

. .

. .