Class 11

Math

3D Geometry

Conic Sections

Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse $49x_{2} +36y_{2} =1.$

Her the donominator of $49x_{2} $is greater than the donominator of $36y_{2} $

Therefore the major axis is along the $x$-axis while the minor axis is along the $y$-axis

On comparing the given equation with $a_{2}x_{2} +b_{2}y_{2} =1$ we obtain $a=7$ and $b=6$

$∴ae=c=a_{2}−b_{2} =49−36 =13 $

Therefore, the coordinates of the foci are $(±13 ,0)$

The coordinates of the vertices are $(±7,0)$

Length of major axis $=2a=14$

Length of minor axis $=2b=12$

Eccentricity $e=$ $ac =$ $713 $

Length of latus rectum $=$ $a2b_{2} =72×36 =772 $