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

CBSE BoardEnglish MediumSTD 11 ScienceMathsSTD 11 - 10.2 parabola,ellipse,hyperbola1 Mark
MCQ
Minimum distance between two points $P$ and $Q$ on the ellipse $\frac{{{x^2}}}{{25}} + \frac{{{y^2}}}{4} = 1$ , if difference between eccentric angles of $P$ and $Q$ is $\frac{{3\pi }}{2}$ , is
  • ✓
    $2\sqrt 2 $
  • B
    $2\sqrt 5 $
  • C
    $\sqrt {29} $
  • D
    $\sqrt {62} $
✓

Answer

Correct option: A.
$2\sqrt 2 $
a
$\mathrm{P}(5 \cos \theta, 2 \sin \theta), \mathrm{Q}(5 \sin \theta,-2 \cos \theta)$

$\mathrm{PQ}=\sqrt{(5 \cos \theta-5 \sin \theta)^{2}+(2 \sin \theta+2 \cos \theta)^{2}}$

$\mathrm{PQ}=\sqrt{29-21 \sin 2 \theta}$

Minmum value of $\mathrm{PQ}=\sqrt{8}=2 \sqrt{2}$

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