Question

Let $P$ and $Q$ be two points on the curves $x^{2}+y^{2}=2$ and $\frac{x^{2}}{8}+\frac{y^{2}}{4}=1$ respectively. Then the minimum value of the length $PQ$ is

• A. $1$
• B. $2-\sqrt{2}$
• C. $2\sqrt{2}$
• D. $\sqrt{2}$

Answer 1

Answer: (B)

The shortest distance $PQ$ occurs along the common normal;
i.e., when $P$ is $\left(0 , \sqrt{2}\right)$ & $Q$ is $\left(0,2\right).$
Hence $\left(P Q\right)_{\text{minimum}}=2-\sqrt{2}$