Verified Solution • 2025–26 Session moderate

QJEEAdv21Ma6e44: JEE Advanced 2021 Mathematics - Class 11 JEEAdv21Ma6e44 Solution: Let E denote the parabola y 2 = 8x. Let P = ( − 2, 4), and let…

Let E denote the parabola y2 = 8x. Let P = (−2, 4), and let Q and Q' be two distinct points on E such that the lines PQ and PQ' are tangents to E. Let F be the focus of E. Then which of the following statements is(are) TRUE?

Multiple Choice Options

  • A The triangle PFQ is a right-angled triangle
  • B The triangle QPQ' is a right-angled triangle
  • C The distance between P and F is 52
  • D F lies on the line joining Q and Q'

Step-by-Step Verified Solution

Given, E : y2 = 8x .... (i)

and P ≡ (−2, 4)

Now, directrix of Eq. (i) is x = −2

JEE Advanced 2021 Paper 2 Online Mathematics - Parabola Question 7 English Explanation
So, point P(−2, 4) lies on the directrix of parabola y2 = 8x. Hence, ∠QPQ′=π2 (by the definition of director circle) and chord QQ' is a focal chord and segment PQ subtends a right angle at the focus.

Slope of PF = −1 (∵ PF ⊥ QQ')

Now, slope of QQ′=2t1+t2=1

∴ PF=(2+2)2+(0+4)2=32=42

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