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If the normal chord of the parabola y^(2...

If the normal chord of the parabola `y^(2)=4 x` makes an angle `45^(@)` with the axis of the parabola, then its length, is

A

8

B

`8sqrt2`

C

4

D

`4sqrt2`

Text Solution

Verified by Experts

The correct Answer is:
B
The equation of a normal to `y^(2)=4x" at "P(t^(2), 2t)` is
`y+tx=2t+t^(3)`
This makes an angle of `45^(@)` with x-axis. Therefore, t=-1. If it culs the parabola at `Q(t_(1)_^(2),2t_(1))`, then
`t_(1)=-t-2/t=3`
Thus, the coordinates of P and Q are (1, -2) and (9, 0) respectively.
`:." "PQ=sqrt(64+64)=8sqrt2`
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