# Thread: how do i graph a hyperbola from the following equation?

1. ## how do i graph a hyperbola from the following equation?

x^2-3y^2+8x-6y+4=0

how do i find the center,transverse axis, vertices, foci and asymptotes from that equation??

2. ## Re: how do i graph a hyperbola from the following equation?

Move all the x terms together, the y terms together, and put the equation into the standard form by completing the square on the x terms and the y terms.

3. ## Re: how do i graph a hyperbola from the following equation?

Originally Posted by alyse2526
x^2-3y^2+8x-6y+4=0

how do i find the center,transverse axis, vertices, foci and asymptotes from that equation??
start by completing the square in x and y ...

$x^2 + 8x + 16 - 3(y^2 + 2y + 1) = -4 + 16 - 3$

$(x + 4)^2 - 3(y + 1)^2 = 9$

$\frac{(x+4)^2}{9} - \frac{(y+1)^2}{3} = 1$

now you have the hyperbola in the form ...

$\frac{(x-h)^2}{a^2} - \frac{(y-k)^2}{b^2} = 1$

go to this page and see how everything is related ...

Hyperbola Formulas