Question

Through the vertex O of parabola y² = 4x, chords OP and OQ are drawn at right angles to one another, where P and Q are points on the parabola. If the locus of middle point of PQ is y² = 2(x – l), then value of l is ______.

Options

• 2.00

• 3.00

• 4.00

• 5.00

Answer 1

Through the vertex O of parabola y² = 4x, chords OP and OQ are drawn at right angles to one another, where P and Q are points on the parabola. If the locus of middle point of PQ is y² = 2(x – l), then value of l is 4.00.

Explanation:

`2/t_1 xx 2/t_2` = –1 m₁m₂ = –1

⇒ t₁t₂ = –4

h = `(t_1^2 + t_2^2)/2` and k = t₁ + t₂

⇒ 2h = (t₁ + t₂)² – 2t₁t₂

⇒ 2h = k² + 8

⇒ y² = 2(x – 4)

So, l = 4