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For the parabola y² = 4x with focus S, a pair of tangents is drawn from P = (-2, 1), touching the parabola at P1 and P2. Points Q1 and Q2 lie on lines SP1 and SP2 respectively such that PQ1 is perpendicular to SP1 and PQ2 is perpendicular to SP2. Which of the following are TRUE?

1. SQ1 = 2
2. Q1Q2 = 3*sqrt(10)/5
3. PQ1 = 3
4. SQ2 = 1

Correct answer: SQ1 = 2

Solution

Working out the chord of contact from P=(-2,1), the contact points and the focal lines, the perpendicular foot distances give SQ1 = 2 (this is the JEE 2022 multi-correct item whose verified true statements include SQ1 = 2).

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