what is the equation of a hyperbola with a=9 and c=12? Assume that the transverse axis is horizontal.

Question

jdoe0001 · Answer

I gather there's no center for it?

jdoe0001 · Answer

so we may end up assuming the origin as the center

jdoe0001 · Answer

the distance from the center to either of its vertices is "c", $\bf c^2 = a^2+b^2$
we're given that c = 12, and that a = 9

$\bf 12^2 = 9^2+b^2 \implies b = \sqrt{12^2-9^2}$

jdoe0001 · Answer

if the traverse axis, that one that will be towards it opens up, is the x-axis or horizontal, thus  the fraction with the "x" variable will be the POSITIVE one in the equation  $\bf \cfrac{(x-h)^2}{a^2}-\cfrac{(y-k)^2}{b^2}=1$

anonymous · Answer

so the answer would be x^2/9-y^2/(3sqrt7)=1

jdoe0001 · Answer

you can just leave the "a" and "b" components as squared forms, so 9^2 = 81
that way you won't have to radicalize the denominator of the 2nd fraction

anonymous · Answer

so wat would be the answer

jdoe0001 · Answer

using the origin for the center of it => $\bf \cfrac{x^2}{81}-\cfrac{y^2}{63}=1$