Question

The length of normal drawn from the point on the axis of the parabola $y^2=8x$ whose distance from the focus is $8$ is equal to

• A. $8$
• B. $6$
• C. $10$
• D. $14$

Answer 1

Answer: (A)

$8$

The length of normal drawn from point on axis of parabola of $y^2=8x$ whose distance from the focus is $8$ is equal to :

Let point be $(h,0)$ and focus is $(2,0)$

Distance $=8=h-2$

$h=10$

Point is $(10,0)$

Equation of normal drawn from $({2t}^2,4t)$ is

$y=-xt+4t++2t^3$

It passes through $(10,0)$

$2t^3+4t-10t=0t=0,\sqrt{3},-\sqrt{3}$

Length of normal from $(6,4\sqrt{3})$ to $(10,0)$ is

$\sqrt{16+48}=8$ Units