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10.2 parabola,ellipse,hyperbola — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHS10.2 parabola,ellipse,hyperbola1 Mark
MCQ
If the eccentricity of the two ellipse $\frac{{{x^2}}}{{169}} + \frac{{{y^2}}}{{25}} = 1$ and $\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} = 1$ are equal, then the value of $a/b$ is
  • A
    $5\over{13}$
  • B
    $6\over{13}$
  • ✓
    $13\over5$
  • D
    $13\over6$
✓

Answer

Correct option: C.
$13\over5$
c
(c) In the first case, eccentricity $e = \sqrt {1 - (25/169)} $

In the second case, $e'\, = \sqrt {1 - ({b^2}/{a^2})} $

According to the given condition,

$\sqrt {1 - {b^2}/{a^2}} = \sqrt {1 - (25/169)} $

$ \Rightarrow \,b/a = 5/13$,   $(\because \,\,a > 0,\,b > 0)$

$⇒ a/b = 13/5.$

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