# Find the equation of a hyperbola, given a point on it and the length of the transverse axis

My textbook has the following question:

The transverse axis of a hyperbola is of length $24$ and the curve passes through the point $(13, 10)$. Find the equation of the hyperbola. Also give the parametric form of your equation.

I'm not sure if there's enough information given to find the formula. I know that the distance from the centre to the vertex will be $12$. Not sure how to find the rest of the equation. Help will be appreciated :)

• Hint: Let the equation be $\frac {x^2}{a^2} - \frac {y^2}{b^2} = 1$. Then $a = 12$. Now since this curve passes through $(13, 10)$, you can find $b$. – Colescu May 6 '16 at 5:05
• There seem to be quite a few missing things here. Is the center at the origin? Is the transverse axis along the x axis? the y axis? Some direction? – Dan Uznanski May 6 '16 at 5:35
• @YuxiaoXie I doubt the assumption , it should be more general. What about the center and orientation of axis? – brainst May 6 '16 at 5:41
• @brainst Sorry, you're right. But usually this kind of exercises will make these assumptions... If you don't make those assumptions then you can't find an equation (without variables). – Colescu May 6 '16 at 5:56