A) a family of hyperbolas
B) a family of circles whose centres are on the y-axis
C) a family of parabolas
D) a family of ellipse
E) a family of circles whose centres are on the x-axis
Correct Answer: E
Solution :
We have, \[y\frac{dy}{dx}+x=c\] On it can be rewritten as \[ydy=(c-x)dx\] On integrating both sides, we get \[\int{y\,\,dy}=\int{(c-x)}\,dx\] \[\frac{{{y}^{2}}}{2}=cx-\frac{{{x}^{2}}}{2}+{{c}_{1}}\] \[\Rightarrow \,\,{{x}^{2}}+{{y}^{2}}\,-2cx={{c}_{1}}\] Which represents a family of circles whose centre is (c, 0) i. e., on the\[x-\]axis.
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