Question

A tangent to an ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ meets the co-ordinate axes in P and Q. The least value of PQ is

• A. $a-b$
• B. $a+b$
• C. $\frac{a+b}{2}$
• D. $2a$

Answer 1

The correct option is B $a+b$

Ellipse: $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$

$T$ be the tangent to ellipse on any point, Let $T$ intersect axis in $P$ and $Q$. we know that the shortest distance between $P$ and $Q$ is equal to sum of semi major axis and semi minor axis. So ${PQ}_{min}=\frac{2a}{2}+\frac{2b}{2}=a+b$