Question

If $P$ is a variable point on the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$, with $A{A}^{\prime }$ as major axis. Then, the maximum value of the area of the $△AP{A}^{\prime }$ is

• A. $ab$ sq unit
• B. $2ab$ sq unit
• C. $\frac{ab}{2}$ sq unit
• D. None of these

Answer 1

The correct option is A $ab$ sq unit

The point P is a variable point on the ellipse that makes a triangle with the endpoints of the major axis. The maximum area would thus be when the Point P lies on one end of the minor axis.
$\therefore$ Required area $=\frac{1}{2}\left(2a\right)b=absqunit$.