Question

Find the equation of a curve passing through the point (–2, 3), given that the slope of the tangent to the curve at any point (x, y) is $\frac{2x}{y^2}$.

Answer 1

Dear student

$$\begin{gathered} \mathrm{If}\mathrm{xdx}=\left({\mathrm{x}}^2+1\right)\mathrm{dy} \\ \mathrm{Simply}\mathrm{cross}\mathrm{multiply}\mathrm{the}\mathrm{terms} \\ \frac{\mathrm{x}}{\left({\mathrm{x}}^2+1\right)}=\frac{\mathrm{dy}}{\mathrm{dx}} \\ \left[\mathrm{reason}:\frac{\mathrm{a}}{\mathrm{b}}=\frac{\mathrm{c}}{\mathrm{d}}\Rightarrow \mathrm{ad}=\mathrm{bc}\right] \\ \mathrm{And}\mathrm{the}\mathrm{reason}\mathrm{behind}\mathrm{footnote}\mathrm{is}\mathrm{not}\mathrm{a}\mathrm{part}\mathrm{of}\mathrm{your}\mathrm{syllabus}\mathrm{will}\mathrm{be}\mathrm{taught} \\ \mathrm{in}\mathrm{higher}\mathrm{classes}. \end{gathered}$$
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