A) a circle with centre on the \[x\]-axis
B) an ellipse with major axis along the\[y\]-axis
C) a circle with centre on the \[y\]-axis
D) a hyperbola with transverse axis along the\[x\]-axis
Correct Answer: A
Solution :
| \[{{x}^{2}}dx+2xydy-{{y}^{2}}dx=0\] |
| \[{{x}^{2}}dx={{y}^{2}}dx-2xydy\] |
| \[({{x}^{2}}-{{y}^{2}})dx+2xydy=0\] |
| \[dx=-\left( \frac{x.2ydy-{{y}^{2}}dx}{{{x}^{2}}} \right)\] |
| Integrals \[x=-\frac{{{y}^{2}}}{x}+c\] |
| \[{{x}^{2}}+{{y}^{2}}=cx.\] |
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