Search any question & find its solution
Question:
Answered & Verified by Expert
If $a x^2+2 h x y+b y^2+2 g x+2 f y+c=0$, then $\frac{d y}{d x}=$
Options:
Solution:
2684 Upvotes
Verified Answer
The correct answer is:
$-\frac{a x+h y+g}{h x-b y+f}$
$a x^2+2 h x y+b y^2+2 g x+2 f y+c=0$
Differentiating w.r.t. x of y, we get
$\begin{aligned} & 2 a x+2 h\left(y+x \frac{d y}{d x}\right)+2 b y \frac{d y}{d x}+2 g+2 f \frac{d y}{d x}=0 \\ & \therefore \frac{d y}{d x}(2 h x+2 b y+2 f)=-(2 a x+2 h y+2 g) \\ & \text { or } \quad \frac{d y}{d x}=-\frac{(a x+h y+g)}{(h x+b y+f)} .\end{aligned}$
Differentiating w.r.t. x of y, we get
$\begin{aligned} & 2 a x+2 h\left(y+x \frac{d y}{d x}\right)+2 b y \frac{d y}{d x}+2 g+2 f \frac{d y}{d x}=0 \\ & \therefore \frac{d y}{d x}(2 h x+2 b y+2 f)=-(2 a x+2 h y+2 g) \\ & \text { or } \quad \frac{d y}{d x}=-\frac{(a x+h y+g)}{(h x+b y+f)} .\end{aligned}$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.