Question

The area of the triangle formed by the tangents from (1,3) to the parabola y² = 4x and their chord of contact is

• A. 15/2
• B. 3√5/2
• C. 5√5/2
• D. 7√5/2

Answer 1

Answer: (C)

5√5/2

Answer 2

The area of the triangle formed by the tangents from (x₁, y₁) to the parabola y² = 4ax and its chord of contact is $\frac{(y_{1}^{2} - 4ax_{1})^{3/2}}{2a}$.

∴ Required area = $\frac{(a - 4)^{3/2}}{2x1}\mspace{6mu} = \mspace{6mu}\frac{5\sqrt{5}}{2}$