Parabola Question 1
Question 1 - 2024 (27 Jan Shift 1)
If the shortest distance of the parabola $y^{2}=4 x$ from the centre of the circle $x^{2}+y^{2}-4 x-16 y+64=0$ is $d$, then $d^{2}$ is equal to :
(1) 16
(2) 24
(3) 20
(4) 36
Show Answer
Answer (3)
Solution
Equation of normal to parabola
$y=m x-2 m-m^{3}$
this normal passing through center of circle $(2,8)$
$8=2 m-2 m-m^{3}$
$m=-2$
So point $P$ on parabola $\Rightarrow\left(am^{2},-2 am\right)=(4,4)$
And $C=(2,8)$
$PC=\sqrt{4+16}=\sqrt{20}$
$d^{2}=20$
