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STD 12 - 9. differential equations — Mathematics STD 12 Science — Question

CBSE BoardEnglish MediumSTD 12 ScienceMathematicsSTD 12 - 9. differential equations1 Mark
MCQ
Curve passing through $(3, 0)$ and satisfying the differential equation $\left( {9 - {x^2}} \right){\left( {\frac{{dy}}{{dx}}} \right)^2} = 9 - {y^2}$ represents
  • A
    Straight line
  • ✓
    circle
  • C
    parabola
  • D
    Ellipse
✓

Answer

Correct option: B.
circle
b
$\left(9-x^{2}\right)\left(\frac{d y}{d x}\right)^{2}=\left(9-y^{2}\right) \Rightarrow \frac{d x}{\sqrt{9-x^{2}}} \pm \frac{d y}{\sqrt{9-y^{2}}}=0$

$\Rightarrow \sin ^{-1}\left(\frac{\mathrm{x}}{3}\right) \pm \sin ^{-1}\left(\frac{\mathrm{y}}{3}\right)=\mathrm{c}$

passes through $(3,0)$

$\Rightarrow \frac{\pi}{2} \pm 0=\mathrm{c}$

$\Rightarrow \sin ^{-1}\left(\frac{x}{3}\right)=\frac{\pi}{2} \pm \sin ^{-1}\left(\frac{y}{3}\right)$

$\Rightarrow \frac{\mathrm{x}}{3}=\sqrt{1-\frac{\mathrm{y}^{2}}{9}} \Rightarrow \mathrm{x}^{2}+\mathrm{y}^{2}=9$

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