Question

If $P\left(\theta \right)$ and $Q\left(\frac{\pi }{2}+\theta \right)$ are two points on the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$, locus of the mid point of $PQ$ is:

• A. $\frac{x^2}{a^2}+\frac{y^2}{b^2}=\frac{1}{2}$
• B. $\frac{x^2}{a^2}+\frac{y^2}{b^2}=2$
• C. $\frac{x^2}{a^2}+\frac{y^2}{b^2}=4$
• D. none of these

Answer 1

The correct option is A $\frac{x^2}{a^2}+\frac{y^2}{b^2}=\frac{1}{2}$