Question

The area of the triangle formed by the tangent and the normal to the parabola $y^2=4ax$, both drawn at the same end of the latus rectum, and the axis of the parabola is

• A. $2\sqrt{2}{a}^2$
• B. $2a^2$
• C. $4a^2$
• D. None of these

Answer 1

The correct option is C

$4a^2$

One end of the latus rectum is P(a, 2a)
The equation of the tangent PT at P(a,2a) is
y.2a = 2a(x+a), i.e., y =x+a.
The equation of normal PN at (a, 2a) is y + x =2a+a, i.e., y + x =3a.

Solving y=0 and y=x+a, we get x=-a, y=0.
Solving y=0, y+x=3a, we get x=3a, y=0.
The area of the triangle with vertices P(a, 2a), T(-a, 0), N(3a, 0) is $4a^2$.