Question

Two tangents $PQ$ and $PR$ are drawn from an exterior point $P(a,b)$ to the ellipse $x^2+2y^2=2$ such that the equation of $QR$ is $x+3y=1.$ Then the value of $a+b$ is

Answer 1

The equation of $QR$ is $T=0$
i.e., $ax+2by=2$
$\Rightarrow \frac{ax}{2}+by=1$
Comparing it with $x+3y=1,$ we get
$a=2,b=3$
$\therefore a+b=5$