Question

The locus of point of intersection of 3 normals to the parabola y^2=4ax , of which two are at rightangle is ​

Answer 1

Step-by-step explanation:

Equation of the lines joining the origin, vertex of the parabola y

2

=4ax, to the point of intersection of the normal and the curve is

y

2

=4ax

2am+am

3

(mx−y)

⇒4amx

2

−4axy−(2am+am

3

)y

2

=0

These are at right angles if

4am−2am−am

3

=0⇒m=±

2