Question

Let $A$ be a point on the $x$-axis Common tangents are drawn from $A$ to the curves $x^2+y^2=8$ and $y^2=16 x$ If one of these tangents touches the two curves at $Q$ and $R$, then $(Q R)^2$ is equal to

• A. 76
• B. 81
• C. 72
• D. 64

Answer 1

The Correct Option is C

The correct answer is (C) : 72
$y=mx+\frac{4}{m}$
$\frac{|\frac{4}{m}|}{\sqrt{1+m^2}}=2\sqrt{2}$
$\therefore m=\pm 1$
$y=\pm x\pm 4$ Point of contact on parabola
Let $m=1,\left(\frac{a}{m^2},\frac{2a}{m}\right)$
$R(4,8)$
Point of contact on circle $Q(-2,2)$
$\therefore (QR{)}^2=36+36=72$