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Question

Find the locus of the point of intersection of two normals to a parabola which are at right angles to one another.

Easy

Solution

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The equation of the normal to the parabola is .

It passes through the point is


Β  Β  Β  Β .....(1)

Let the roots of the above equation be . Let the perpendicular normals correspond to the values of and so that .

From equation 1,

Since,

Since is a root of equation 1, we have




Hence, the locus of is .

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