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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
The differential equation $\frac{{dx}}{{dy}}= \frac{{3y}}{{2x}}$ represents a family of hyperbolas (except when it represents a pair of lines) with eccentricity :
  • A
    $\sqrt {\frac{5}{3}} $
  • B
    $\sqrt {\frac{5}{2}} $
  • C
    $ \sqrt {\frac{3}{5}} $
  • ✓
    both $(A)$ and $(B)$
✓

Answer

Correct option: D.
both $(A)$ and $(B)$
d
$ x^2 =\frac{{3{y^2}}}{2} + c $

if $c$ is positive $ \Rightarrow $ $e =\sqrt {\frac{5}{3}} $ 

if $c$ is negative $\Rightarrow$ $ e = \sqrt {\frac{5}{2}} $

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