Question

If the normal at the point (1, 2) on the parabola y² = 4x meets the parabola again at the point (t², 2t), then t is equal to ______.

Options

• 1

• –1

• 3

• –3

Answer 1

If the normal at the point (1, 2) on the parabola y² = 4x meets the parabola again at the point (t², 2t), then t is equal to –3.

Explanation:

Use t₁ + t₂ = `-2/"t"_1`  ...(i)

Here 2at₁ = 2

⇒ 2.1.t₁ = 2

⇒ t₁ = 1 and 2at₂ = 2t

⇒ 2.1.t₂ = 2.5

⇒ t₂ = t

From (i) 1 + t = `-2/1`

= –2

⇒ t = –3