Question

If $a{x}^2+2hxy+b{y}^2=1$, then $\frac{dy}{dx}$ equals

• A. $\frac{hx+by}{ax+hy}$
• B. $\frac{ax+hy}{hx+by}$
• C. $\frac{ax+hx}{hy+by}$
• D. $\frac{-\left(ax+hy\right)}{hx+by}$

Answer 1

Answer: (D)

Given $a{x}^2+2hxy+b{y}^2=1$
Differentiating $w$.$r$.$t$. $x$, we get
$2ax+2h\left(x\frac{dy}{dx}+y\right)+2by\frac{dy}{dx}=0$
$\Rightarrow \frac{dy}{dx}=-\left(\frac{ax+hy}{hx+by}\right)$