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If two normals to a parabola y^2 = 4ax i...

If two normals to a parabola `y^2 = 4ax` intersect at right angles then the chord joining their feet pass through a fixed point whose co-ordinates are:

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equation of parabola
`y^2=4ax`
co-ordinates of P`(at_1^2,2at_1)`
co-ordinates of q`(at_2^2,2at_2)`
slope of normal=-t
slope at `M_(N1)=-t_1`
slope at `M_(N2)=-t_2`
we know N1 and N2 are perpendicular
...
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