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At what point on the parabola y^2=4x the...

At what point on the parabola `y^2=4x` the normal makes equal angle with the axes? `(4,4)` (b) `(9,6)` (d) `(4,-4)` (d) `(1,+-2)`

A

(4,4)

B

(9,6)

C

(4,-4)

D

`(1,pm2)`

Text Solution

Verified by Experts

The correct Answer is:
D
(4) We have a=1.
Normal at `(m^(2),-2m)" is "y=mx-2-m^(3)`
Given that normal makes equal angle with the axes, its slope is `m=pm1`.
Therefore, point P is `(m^(2),-2m)-=(1,pm2)`.
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