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Question

The locus of point of intersection of two normals drawn to the parabola which are at right angles is

A

B

C

D

Medium

Solution

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Correct option is
A

The given parabola is 
Let denote the parameter, then the equation of the normal to this parabola is given by 
Now this normal passes through the point then
.......
Let  be the roots of this equation. 
Let the perpendicular normals correspond to the values of 
So,
Now from equation
gives 
Since  is a root of equation , we have

So locus of is 

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