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JEE Main 20205 SeptemberMorning Shift
Exam
JEE Main
Year
2020
Date
5 September
Shift
Morning Shift
Subject
Mathematics
Chapter
Ellipse

JEE Main 2020 · 5 September · Morning Shift · Mathematics · Ellipse

If the co-ordinates of two points A and B are ( 7 , 0 ) and ( - 7 ,...

If the co-ordinates of two points AA and BB are (7,0)( \sqrt{7}, 0 ) and (−7,0)( - \sqrt{7}, 0 ) respectively and PP is any point on the conic, 9x2+16y2=144,9{x}^{2} + 16{y}^{2} = 144, then PA+PBPA + PB is equal to :

Options

  1. A1616
  2. B88
  3. C66
  4. D99

Correct answer

B. 88

Step-by-step solution

For ellipse x216+y29=1\dfrac{{x}^{2}}{16} + \dfrac{{y}^{2}}{9} = 1

Comparing with, standard equation of ellipse x2a2+y2b2=1\dfrac{{x}^{2}}{{a}^{2}} + \dfrac{{y}^{2}}{{b}^{2}} = 1, we get

a=4,b=3a = 4, b = 3.

∴e=1−916=74∴ e = \sqrt{1 - \dfrac{9}{16}} = \dfrac{\sqrt{7}}{4}
Since, AA and BB are foci

Therefore, PA+PB=2aPA + PB = 2a

=2×4=8= 2 \times 4 = 8.

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