Ask Me Help Desk - Write an equation of a hyperbola given foci are (3,5), (3,-3), vertex (3,4)

Quote:

Originally Posted by jennylp

write and equation of a hyperbola, given foci is (3,5), (3,-3), vertex is (3,4)

Since one vertex is given as (3,4), the other is at (3,-2).

There are 6 units between the vertices. That means the center is at (3,1).

c is the distance from the center to the foci. A and b are the lengths of the semi-major and semi-minor axes.

$b=\sqrt{c^{2}-a^{2}}$

$c=4, \;\ a=3$

$b=\sqrt{4^{2}-3^{2}}=\sqrt{16-9}=\sqrt{7}$

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

$\frac{(y-1)^{2}}{9}-\frac{(x-3)^{2}}{7}=1$

Unless you have a calcualtor that graphs conics, we must solve for y to graph.