Question

If y₁, y₂ are the ordinates of two points P and Q on the parabola and y₃ is the ordinate of the point of intersection of tangents at P and Q, then

• A. y₁, y₂, y₃ are in AP
• B. y₁, y_­3, y₂ are in AP
• C. y₁, y₂, y₃ are in GP
• D. y₁, y₃, y₂ are in GP

Answer 1

Answer: (B)

y₁, y_­3, y₂ are in AP

Answer 2

In a parabola, the point of intersection of tangents at t₁ and t₂ is (at₁t₂, a(t₁+t₂)).

Let P, Q represents t₁ and t₂

∴ y₁ = 2at, y₂ = 2at₂ ⇒ y₃ =a(t₁+t₂)

We can prove that y₁ + y₂ = 2y₃

⇒ $y_{1},y_{3},y_{2}$ are in A.P.