Conic Sections Question 150
Question: At what point on the parabola $ y^{2}=4x $ , the normal makes equal angles with the co-ordinate axes
[RPET 1994]
Options:
A) (4, 4)
B) (9, 6)
C) (4, -4)
D) (1, -2)
Show Answer
Answer:
Correct Answer: D
Solution:
The equation of a normal to $ y^{2}=4x $ at $ (m^{2},-2m) $ is $ y=mx-2m-m^{3}. $ If the normal makes equal angles with the coordinates axes, then $ m=\tan \frac{\pi }{4}=1. $ Thus, the required point is (1, - 2).
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