Question

Prove that two straight line one tangent to parabola y2=4a(x+a) and the other parabola

Answer 1

Slope of tangent at any point is 

dy/dx = 2a/y

Slope of normal at that point is

-y/2a = m (say)

⇒ Point of contact of a normal having slope ‘m’ with the Parabola

yy2 = 4ax is (amy2, – 2am) 

So, equation of normal at this point is 

y + 2am = m (x – amy2)

or y = mx – 2am – amy3.