Question

If from a point $P,$ tangents $PQ$ and $PR$ are drawn to the ellipse $\frac{x^2}{2}+y^2=1,$ such that equation of $QR$ is $x+3y=1,$ then the coordinates of $P$ is

• A. $(1,-2)$
• B. $(2,3)$
• C. $(1,2)$
• D. $(2,-3)$

Answer 1

The correct option is B $(2,3)$

Equation of ellipse is $\frac{x^2}{2}+y^2=1$
Let coordinates of $P$ be $(h,k)$, then equation of $QR$ is $T=0$
$\Rightarrow \frac{hx}{2}+ky=1...\left(i\right)$
Also equation of $QR$ is given as $x+3y=1...\left(ii\right)$
$\because \left(i\right)$ and $\left(ii\right)$ are representing the same line equation with equal constant term.
$\therefore h=2$ and $k=3$
$\therefore$ Coordinates of $P$ is $(2,3).$