Question

The mid point of the line joining the points A(7,3) and B(-1, -5) is C. The values of k for which the
straight line joining C to the point P is perpendicular to AB are

Answer 1

Given that normal intersect at point A,B and C on parabola y^2 =4x

The parabola intersect at P(h,K)

y^2 =4x,h→x,K→y.

∴x=y 2/4

i.e,2y  dx/ dy  =4

⇒  dx /dy  = 2/y

Equation of normal parring through (h,K)

y-y1/x-x1=y-K/x-H=-1dy

By solving ,and substituting values of (h,K)→(x,y)

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