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Let E be the parabola y² = 8x with focus F. From the external point P = (-2, 4), two tangents touch E at distinct points Q and Q'. Which of the following statements is/are TRUE?
- Triangle PFQ is right-angled
- Triangle QPQ' is right-angled
- The distance PF equals 5*sqrt(2)
- F lies on line QQ'
Correct answer: Triangle PFQ is right-angled
Solution
Since P is on the directrix, PQ and PQ' are perpendicular and the focal chord property makes triangle PFQ right-angled at F (a known JEE Advanced 2021 result with multiple correct options).
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