Question

Find the length of the line-segment joining the vertex of the parabola y² = 4ax and a point on the parabola where the line-segment makes an angle q to the x-axis.

Answer 1

Equation of an ellipse is y² = 4ax, whereas

Length of latus rectum = 4a

Let the point on parabola be (i,j)

From the figure, slope of OP = tan θ = j/i

j = itanθ

j² = i² tan² θ 

[Squaring the above mentioned equation] ------- (i)

j² = 4ai------- (ii)

Equating the equations, {(i) & (ii)}