Class 11

Math

3D Geometry

Conic Sections

Find the equation for the ellipse that satisfies the given conditions:

Vertices $(±6,0)$, foci $(±4,0).$

Clearly, the vertices are on the $x$-axis.

Therefore, the equation of the ellipse will be of the form $a_{2}x_{2} +b_{2}y_{2} =1$, where $a$ is the semi-major axis.

Also, $a=6,ae=4⇒e=32 $

We know that $b_{2}=a_{2}(1−e_{2})=a_{2}−a_{2}e_{2}=36−16=20$

Thus, the equation of the ellipse is $36x_{2} +20y_{2} =1$