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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 eccentricities of the hyperbolas $\frac{{{x^2}}}{{{a^2}}} - \frac{{{y^2}}}{{{b^2}}} = 1$ and $\frac{{{y^2}}}{{{b^2}}} - \frac{{{x^2}}}{{{a^2}}} = 1$ be e and ${e_1}$, then $\frac{1}{{{e^2}}} + \frac{1}{{e_1^2}} = $
  • ✓
    $1$
  • B
    $2$
  • C
    $3$
  • D
    None of these
✓

Answer

Correct option: A.
$1$
a
(a) $e = \sqrt {1 + \frac{{{b^2}}}{{{a^2}}}} $

==> ${e^2} = \frac{{{a^2} + {b^2}}}{{{a^2}}}$

==> ${e_1} = \sqrt {1 + \frac{{{a^2}}}{{{b^2}}}} $

==> $e_1^2 = \frac{{{b^2} + {a^2}}}{{{b^2}}}$

==> $\frac{1}{{e_1^2}} + \frac{1}{{{e^2}}} = 1$.

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