JEE Main 2023 (Online) 29th January Evening ShiftQuestion 1
A circle with centre $(2,3)$ and radius $4$ intersects the line $x+y=3$ at the points $P$ and $Q$. If the tangents at $P$ and $Q$ intersect at the point $S(\alpha,\beta)$, then $4\alpha-7\beta$ is equal to
Circle
Answer$11$
Solution
$S$ is the pole of $x+y=3$: the polar $(\alpha-2)(x-2)+(\beta-3)(y-3)=16$ must coincide with $x+y=3$, so $\alpha-2=\beta-3=t$ with $\frac{16+5t}{t}=3$, $t=-8$. Hence $S=(-6,-5)$ and $4\alpha-7\beta=11$.