Question

Let P be a point on the parabola y2 = 4ax, where a > 0. The normal to the parabola at P meets the x -axis at a point Q. The area of the triangle PFQ where F is the focus of the parabola, is 120. If the slope m of the normal and a are both positive integers, then the pair (a, m) is

• A. (2,3)
• B. (1,3)
• C. (2,4)
• D. (3,4)

Answer 1

Answer: (A)

(2,3)

Answer 2

Equation of normal at P(am2, –2am) is y = mx – 2am – am3
⇒ Area of ∆PFQ = 1/2(a + am2) x 2am = 120
a2m(1 + m2) = 120 Pair (a, m) ≡ (2, 3) satisfies above equation.