Class 11

Math

3D Geometry

Conic Sections

Find the equation of the hyperbola satisfying the give conditions: Foci $(0,±13)$ the conjugate axis is of length $24$

Here the foci are on the $y$-axis.

Therefore, the equation of the hyperbola is of the form $a_{2}y_{2} −b_{2}x_{2} =1$

Since the foci are $(0,±13)⇒ae=c=13$

Since the length of the conjugate axis is $24$,$⇒2b=24⇒b=12$

We know that $a_{2}+b_{2}=c_{2}$

$∴a_{2}+12_{2}=13_{2}$

$⇒a_{2}=169−144=25$

Thus the equation of the hyperbola is $25y_{2} −144x_{2} =1$