MCQ
If ${x^3} + {y^3} - 3axy = 0$, then ${{dy} \over {dx}}$ equals
- ✓${{ay - {x^2}} \over {{y^2} - ax}}$
- B${{ay - {x^2}} \over {ay - {y^2}}}$
- C${{{x^2} + ay} \over {{y^2} + ax}}$
- D${{{x^2} + ay} \over {ax - {y^2}}}$
Differentiate w.r.t. $x,$
$3{x^2} + 3{y^2}.\frac{{dy}}{{dx}} - 3a\left( {x\frac{{dy}}{{dx}} + y} \right) = 0$
$ \Rightarrow $ $3({x^2} - ay) + 3\frac{{dy}}{{dx}}({y^2} - ax) = 0$
$ \Rightarrow $ $\frac{{dy}}{{dx}} = \frac{{ay - {x^2}}}{{{y^2} - ax}}$.
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