Question

Tangents are drawn from a point P to the parabola y² = 8x such that the slope of one tangent is twice the slope of other. The locus of P is

• A. A circle
• B. A straight line
• C. A parabola
• D. An ellipse

Answer 1

Answer: (C)

A parabola

Answer 2

y² = 8x, a = 2 ̃ 2y$\frac{dy}{dx} = 8$ ̃ $\frac{dy}{dx} = \frac{4}{y}$

m₁ = 2m₂ ̃ 1/t₁ = 2t₂ … (i)

K = a(t₁ + t₂) = 2(t₁ + t₂) = 2(3t₁) ̃ t₁ = K/6

̃ t₂ = K/3

Now, h = at₁t₂ ̃ h = 2 × k/6 × k/3 ̃ k² = 9h

Lows of P y² = 9x