Question

If two tangents drawn from the point (a, b) to the parabola

y² = 4x be such that the slope of one tangent is double of the other then-

• A. b = $\frac{2}{9}$a²
• B. a = $\frac{2}{9}$b²
• C. 2a = 9b²
• D. None

Answer 1

Answer: (B)

a = $\frac{2}{9}$b²

Answer 2

Any tangent to the parabola y² = 4x is

y = mx + $\frac{1}{m}$. It passes though (a, b) if

b = ma + $\frac{1}{m}$ or am² – bm + 1 = 0.

It will have roots m₁, 2m₁ if

m₁ + 2m₁ = $\frac{\beta}{\alpha}$, m₁ . 2m₁ = $\frac{1}{\alpha}$ Ž 2 . $\left( \frac{\beta}{3\alpha} \right)^{2}$ = $\frac{1}{\alpha}$.