Class 11

Math

3D Geometry

Conic Sections

Find the equation for the ellipse that satisfies the given conditions: $b=3,ae=4$ centre at the origin; foci on the $x$- axis.

Since the foci are on the $x$-axis $⇒$ the major axis is along 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.

Accordingly $b=3,ae=4.$

It is known that $a_{2}=b_{2}+ae_{2}$

$∴a_{2}=3_{2}+4_{2}=9+16=25$

$⇒a=5$

Thus, the equation of the ellipse is $5_{2}x_{2} +3_{2}y_{2} =1$

$⇒25x_{2} +9y_{2} =1.$