Question

Consider the parabola y² = 4x. A ≡(4, -4) and B ≡ (9, 6) be two fixed points on the parabola. Let 'C' be a moving point on the parabola between A and B such that the area of triangle ABC is maximum, then coordinate of 'C' is

• A. (1/4, 1)
• B. (4, 4)
• C. (3, 2$\sqrt{3}$)
• D. (3, −2$\sqrt{3}$)

Answer 1

Answer: (A)

(1/4, 1)

Answer 2

Area of triangle ABC is maximum if CD is maximum, because AB is fixed. That means tangent drawn to parabola at 'C should be parallel to AB. Sloe of AB = $\frac { 6 + 4 } { 9 - 4 }$ =2.