Question

P(t = 2) is a point on the parabola $y^2=4ax$. What is the point of the intersection of tangent at P and the directrix of the parabola?

• A. (10, 10)
• B. (-10, 15)
• C. (15, 10)
• D. (0, 0)

Answer 1

The correct option is B (-10, 15)

The equation of the tangent at 'p' is,

$ty=x+a{t}^2$

here

t=2;a=10

i.e.,2y=x+40 ..........(1)

Directrix

x+10=0 ............(2)

Solving (1) and (2)

2y=-10+40

y=15

$\therefore Requiredpoint\equiv (-10,15)$