• # question_answer The curve amongst the family of curves represented by the differential equation, $({{x}^{2}}-{{y}^{2}})dx+2xy$$dy=0$ which passes through $(1,1),$ is: 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

 ${{x}^{2}}dx+2xydy-{{y}^{2}}dx=0$ ${{x}^{2}}dx={{y}^{2}}dx-2xydy$ $({{x}^{2}}-{{y}^{2}})dx+2xydy=0$ $dx=-\left( \frac{x.2ydy-{{y}^{2}}dx}{{{x}^{2}}} \right)$ Integrals          $x=-\frac{{{y}^{2}}}{x}+c$ ${{x}^{2}}+{{y}^{2}}=cx.$