If x3+y3-3axy=0 , then (dy/dx) equals

Question

If x3+y3-3axy=0 , then (dy/dx) equals (A)  (ay-x2/y2-ax)  (B)  (ay-x2/ay-y2)  (C)  (x2+ay/y2+ax)  (D)  (x2+ay/ax-y2)

Tardigrade Admin · Accepted Answer

Given, x3+y3-3 a x y=0 On differentiating w.r.t. x, we get 3 x2+3 y2 ⋅ (d y/d x)-3 a(x (d y/d x)+y)=0 ⇒ 3(x2-a y)+3 (d y/d x)(y2-a x)=0 ⇒ (d y/d x)=(a y-x2/y2-a x)

Q. If $x^{3} + y^{3} - 3 a x y = 0$ , then $\frac{d y}{d x}$ equals

$\frac{a y - x ^{2}}{y ^{2} - a x}$

$\frac{a y - x ^{2}}{a y - y ^{2}}$

$\frac{x ^{2} + a y}{y ^{2} + a x}$

$\frac{x ^{2} + a y}{a x - y ^{2}}$

Given, $x^{3} + y^{3} - 3 a x y = 0$
On differentiating w.r.t. $x,$ we get
$3 x^{2} + 3 y^{2} \cdot \frac{d y}{d x} - 3 a (x \frac{d y}{d x} + y) = 0$
$\Rightarrow 3 (x^{2} - a y) + 3 \frac{d y}{d x} (y^{2} - a x) = 0$
$\Rightarrow \frac{d y}{d x} = \frac{a y - x ^{2}}{y ^{2} - a x}$

Q. If x3+y3−3axy=0 , then dxdy​ equals

y2−axay−x2​

ay−y2ay−x2​

y2+axx2+ay​

ax−y2x2+ay​