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9. differential equations — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths9. differential equations1 Mark
MCQ
Curve which passes through point $\left( {\sqrt 2 ,1} \right)$ and satisfying the differentiable equation $\frac{{dy}}{{dx}} = \frac{{2x}}{{3y}}$ , represents
  • A
    a circle
  • B
    a parabola
  • C
    an ellipse
  • ✓
    a hyperbola
✓

Answer

Correct option: D.
a hyperbola
d
$2 x d x-3 y d y=0$

$x^{2}-\frac{3 y^{2}}{2}=C$

$2-\frac{3}{2}=C$

$\therefore C=\frac{1}{2}$

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