Class 11

Math

3D Geometry

Conic Sections

Find the coordinates of the foci, the vertices the eccentricity and the length of latus rectum of the hyperbola $16x_{2}−9y_{2}=576$

$⇒36x_{2} −64y_{2} =1$

$⇒6_{2}x_{2} −8_{2}y_{2} =1...(1)$

On comparing equation (1) with the standard equation of hyperbola, $a_{2}x_{2} −b_{2}y_{2} =1$,

we obtain $a=6,b=8⇒e=1+a_{2}b_{2} =1+3664 =35 $

Therefore, the coordinates of the foci are $(±10,0)$

The coordinates of the vertices are $(±6,0)$

Eccentricity $e=35 $

Length of latus rectum $=$ $a2b_{2} =62×64 =364 $