Question

If $y^2+b^2=2xy$, then $\frac{dy}{dx}$ equals

• A. $\frac{1}{xy-b^2}$
• B. $\frac{y}{y-x}$
• C. $\frac{xy-b^2}{{(y-x)}^2}$
• D. $\frac{xy-b^2}{y}$

Answer 1

Answer: (B), (C)

The correct options are
B $\frac{y}{y-x}$
C $\frac{xy-b^2}{{(y-x)}^2}$

$y^2+b^2=2xy\Rightarrow$
differentiating both sides w.r.t. $x$
$\Rightarrow 2y\frac{dy}{dx}=2(y+x\frac{dy}{dx})$
$\Rightarrow \frac{dy}{dx}=\frac{y}{y-x}=\frac{y(y-x)}{(y-x{)}^2}=\frac{xy-b^2}{(y-x{)}^2}$, using (1)