At what point on the parabola y^2 = 4x, the normal makes equal an… - Vidyadip

MCQ

At what point on the parabola ${y^2} = 4x$, the normal makes equal angles with the co-ordinate axes

A
$(4, 4)$
B
$(9, 6)$
C
$(4, -4)$
✓
$(1, -2)$

✓

Answer

Correct option: D.

$(1, -2)$

d
(d) 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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