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JEE Main 201815 AprilEvening ShiftOnline
Exam
JEE Main
Year
2018
Date
15 April
Shift
Evening Shift
Mode
Online
Subject
Mathematics
Chapter
Parabola

JEE Main 2018 · 15 April · Evening Shift · Online · Mathematics · Parabola

Tangents drawn from the point (-8,0) to the parabola y^2=8 x touch...

Tangents drawn from the point (−8,0)(-8,0) to the parabola y2=8xy^2=8 x touch the parabola at PP and QQ. If FF is the focus of the parabola, then the area of the triangle PFQP F Q (in sq. units) is equal to

Options

  1. A48
  2. B32
  3. C24
  4. D64

Correct answer

A. 48

Step-by-step solution

Equation of the chord of contact PQP Q is given by: T=0 or T≡yy1−4(x+x1),where(x1,y1)≡(−T \equiv y y_1-4 \left(x+x_1\right), where \left(x_1, y_1\right)\equiv(-8,0)\thereforeEquationbecomes:Equation becomes:x=8\&ChordofcontactisChord of contact isx=8\thereforeCoordinatesofpointCoordinates of pointP and Qareare(8,8) and (8,-8)andfocusoftheparabolaisand focus of the parabola isF(2,0)\thereforeAreaoftriangleArea of triangleP Q F=12×F=\frac{1}{2} \times(8-2) \times(8+8)=48sq.unitssq. units
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