If x^3 + y^3 - 3axy = 0, then dy dx equals - Vidyadip

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
${{{x^2} + ay} \over {ax - {y^2}}}$

✓

Answer

Correct option: A.

${{ay - {x^2}} \over {{y^2} - ax}}$

a
(a) ${x^3} + {y^3} - 3axy = 0$

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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