Question

The tangents at P, Q, R on the parabola y² = 4ax make angles 30⁰, 45⁰, 60⁰ with the x-axis. Then their ordinates form a

• A. A.P.
• B. G.P.
• C. H.P.
• D. A.G.P

Answer 1

Answer: (B)

G.P.

Answer 2

Let P(t₁), Q(t₂) and R(t₃)

The slope of the tangent at P = $\frac{1}{t_{1}} = \tan 30^{o} = \frac{1}{\sqrt{3}}$

⇒ t₁ = $\sqrt{3}$

Slope of the tangent at Q = $\frac{1}{t_{2}} = \tan 45^{o}$

⇒ t₂ = 1

Slope of the tangent at R = $\frac{1}{t_{3}} = \tan 60^{o}$

⇒ t₃ = 1/$\sqrt{3}$

∴ t₁, t₂, t₃ are in GP

⇒ 2at₁, 2at₂, 2at₃ are in GP

⇒ y₁, y₂, y₃ are in GP