Question

Let $C$ be a conic which is reflection of hyperbola $\frac{( x -2)^2}{3}-\frac{( y -1)^2}{4}=-1$ in the line $x + y -1=0$.
Let locus of point of intersection of perpendicular tangents to conic $C$ be $S$. From a point $P (4$, 2), pair of tangents $P A$ and $P B$ are drawn to $S$. Diameter of circumcircle of $\triangle P A B$ will be

• A. $\frac{5}{2}$
• B. 5
• C. 10
• D. 20

Answer 1

Answer: (B)

Locus of point of intersection of perpendicular tangents will be director circle i.e. $x^2+(y+1)^2=4-3$
$\Rightarrow x^2+(y+1)^2=1$

Clearly, circumcircle of $\triangle PAB$ will be circle with diameter $PC$.
$\therefore $ Diameter $= PC =5$