The equation of a hyperbola is like this:
x^2/a^2 - y^2/b^2 = 1

my problem is this.. I don't know what am I going to do with this equation > 4x^2 - y^2 = 4y
to become same as the equation above.. I am confused because of the 4y..
After that, I will find the center, vertices, foci and asymptote of that equation.

Another problem. (in ellipse)
Same as the above problem about the equation.
4x^2 + y^2 = 8x
Because of 8x there, I don't know how am I going to do that same like this:
(x-h)^2/a^2 + (y-k)^2/b^2=1

After that, I will also going to find its center, foci and semi axes.

Hope you can help me. Thanks! :)

Complete the square.

For the ellipse. 4x^{2}+y^{2}=8x

4x^{2}-8x+y^{2}=0

4(x^{2}-2x)+y^{2}=0

Complete the square:

4(x^{2}-2x+1)+y^{2}=4

Factor what's in the parentheses and divide by 4:

4(x-1)^{2}+y^{2}=4

(x-1)^{2}+\frac{y^{2}}{4}=1

There is the ellipse equation. See the center and lengths of axes?

Try the same method with your hyperbola

Here is a graph of your ellipse:

Thanks for your help galactus! :)