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

Answer: (C)

72

Answer 2

The correct answer is (C) : 72
y=mx+m4​
1+m2​∣m4​∣​=22​
∴m=±1
y=±x±4 Point of contact on parabola
Let m=1,(m2a​,m2a​)
R(4,8)
Point of contact on circle Q(−2,2)
∴(QR)2=36+36=72