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STD 11 - 10.2 parabola,ellipse,hyperbola — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 11 - 10.2 parabola,ellipse,hyperbola4 Marks
MCQ
$P$ is a variable point on the ellipse $\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} = 1$ with $AA'$ as the major axis. Then the maximum value of the area of $\Delta APA'$ is
  • ✓
    $\left| {ab} \right|$
  • B
    $\left| {\frac{{ab}}{2}} \right|$
  • C
    $\left| {2ab} \right|$
  • D
    $\left| {\frac{{ab}}{4}} \right|$
✓

Answer

Correct option: A.
$\left| {ab} \right|$
a
Maximum area corresponds to when $P$ is at either end of the minor exis and hence area for such position of $P = \frac{1}{2}2ab = ab$

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