# how do i find an equation for the hyperbola with the given information

• Dec 3rd 2012, 10:03 PM
alyse2526
how do i find an equation for the hyperbola with the given information
i have absolutely no clue how to figure this one out

focus at (-4,0); vertices at (-4,4) and (-4,2)
• Dec 3rd 2012, 10:42 PM
earboth
Re: how do i find an equation for the hyperbola with the given information
Quote:

Originally Posted by alyse2526
i have absolutely no clue how to figure this one out

focus at (-4,0); vertices at (-4,4) and (-4,2)

1. Draw a sketch.

2. Determine the coordinates of the midpoint of the hyperbola. $\displaystyle (M(x_M , y_M))$

3. Determine the value of the excentricity e (that's the distance between the midpoint and one focus)

4. Determine the length of the axis a (that's the distance between the midpoint and one vertex)

5. Calculate the length of the axis b using $\displaystyle e^2=a^2+b^2$

6. Use the equation

$\displaystyle \frac{(x-x_M)^2}{a^2} - \frac{(y-y_M)^2}{b^2}=1$