Question

The angle between the tangents drawn from the origin to the parabola y^2=4a(x-a) is

Answer 1

Let the equation of the tangent y=mx (since c=0)

Putting y=mx in the eqn of parabola

m^2x^2=4a(x-a)

m^2x^2-4ax+4a^2=0

D=0 (since the tangent cuts the parabola at 1 pt...roots are equal)

(4a)^2=4(4a^2)m^2

m=+1 or m=-1

we get the slopes of the 2 tangents as +1 and -1

Product of slopes =-1

Therefore angle between them is 90