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At what point on the parabola $y^2=4 x$, the normal makes equal angles with the co-ordinate axes
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$(1,-2)$
The equation of a normal to $y^2=4 x$ at $\left(m^2,-2 m\right)$ is $y=m x-2 m-m^3$. 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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