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
- AStraight line
- ✓circle
- Cparabola
- DEllipse
$\Rightarrow \sin ^{-1}\left(\frac{\mathrm{x}}{3}\right) \pm \sin ^{-1}\left(\frac{\mathrm{y}}{3}\right)=\mathrm{c}$
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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