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JEE Advanced 2021Paper 2

Exam: JEE Advanced
Year: 2021
Paper: Paper 2
Subject: Mathematics
Chapter: Parabola

JEE Advanced 2021 · Paper 2 · Mathematics · Parabola

Let E denote the parabola y ^ 2 = 8x . Let P = (- 2, 4) , and let Q...

Let

E

denote the parabola

{y}^{2} = 8x .

Let

P = \left(- 2, 4\right)

, and let

Q

and

{Q}^{'}

be two distinct points on

E

such that the lines

PQ

and

P{Q}^{'}

are tangents to

E

. Let

F

be the focus of

E

. Then which of the following statements is (are) TRUE? Let E denote the parabola y ^ 2 = 8x . Let P = (- 2, 4) , and let Q and Q ^ ' be two distinct points on E such that the

Let E denote the parabola y ^ 2 = 8x . Let P = (- 2, 4) , and let Q and Q ^ ' be two distinct points on E such that the

Options

AThe triangle $PFQ$ is a right-angled triangle
BThe triangle $QP{Q}^{'}$ is a right-angled triangle
CThe distance between $P$ and $F$ is $5\sqrt{2}$
D $F$ lies on the line joining $Q$ and ${Q}^{'}$

Correct answer

A. The triangle $PFQ$ is a right-angled triangle

Step-by-step solution

Let E denote the parabola y ^ 2 = 8x . Let P = (- 2, 4) , and let Q and Q ^ ' be two distinct points on E such that the

${y}^{2} = 8x$

$⇒ a = 2,$ Focus $F\left(2, 0\right),$ and Directrix $x = - 2$

$∵ P\left(- 2, 4\right)$ lies on directrix

$⇒ Q{Q}^{'}$ will be a focal chord and tangents are mutually perpendicular.

$⇒ \DeltaQP{Q}^{'}$ is right angled.

Also the portion between point of contact and directrix of parabola subtends right angle at the focus.

So, $△ PFQ$ is a right- angled triangle.

$PF = \sqrt{{\left(- 2 - 2\right)}^{2} + {\left(4 - 0\right)}^{2}} = 4\sqrt{2}$

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