Class 11

Math

3D Geometry

Conic Sections

Find the equation of the hyperbola satisfying the given conditions: Foci $(±5,0)$ the

transverse axis is of length $8$

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

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

Since the foci are $(±5,0)⇒ae=c=5$

Since the length of the transverse axis is $8$, $⇒2a=8⇒a=4$

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

$4_{2}+b_{2}=5_{2}$

$⇒b_{2}=25−16=9$

Thus the equation of the hyperbola is $16x_{2} −9y_{2} =1$