JEE Mains Model Paper 4

Given equation of the parabola is y2 = 4ax.
Let the point on the parabola be p(z1,y1)
From the figure, slope of OP = tan θ =

y1

x1

..... (i)
Now, OP = √x12+y12 = √x12+tan2θx12 = √x12sec2θ = x1 secθ .... (ii)
From(i)and (ii), we have
tan2θx12 = 4ax1 ⇒ x1 =

4a

tan2θ

OP =

4acosθ

sin2θ