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JEE Main 20206 SeptemberMorning Shift
Exam
JEE Main
Year
2020
Date
6 September
Shift
Morning Shift
Subject
Mathematics
Chapter
Ellipse

JEE Main 2020 · 6 September · Morning Shift · Mathematics · Ellipse

Which of the following points lies on the locus of the foot of...

Which of the following points lies on the locus of the foot of perpendicular drawn upon any tangent to the ellipse, x24+y22=1\dfrac{{x}^{2}}{4} + \dfrac{{y}^{2}}{2} = 1 from any of its foci?

Options

  1. A(−2,3)( - 2, \sqrt{3} )
  2. B(−1,2)( - 1, \sqrt{2} )
  3. C(−1,3)( - 1, \sqrt{3} )
  4. D(1,2)( 1, 2 )

Correct answer

C. (−1,3)( - 1, \sqrt{3} )

Step-by-step solution

Foot of perpendicular from focus upon any tangent lies on auxiliary circle

So equation of locus is: x2+y2=4{x}^{2} + {y}^{2} = 4

Now verify option

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