Question

if ax2 + 2hxy +by2 + 2gx + 2fy +c =0. Find dy/dx

Answer 1

Hope it will be helpful for you

Answer 2

Concept :

We  first recall the concept of  differentiation to solve this question.

Differentiation refers to the derivative of a dependent variable with respect  to the independent variable in a Function by differentiating each term seperately .

Given:

The equation is  $ax^{2} + 2hxy +by^{2} + 2gx + 2fy +c =0$                     (1)

To find:

The derivative $\frac{dy}{dx}$ of the given equation

Solution:

On Differentiating equation (1) with respect to x

         $\frac{d}{dx}(ax^{2} + 2hxy +by^{2} + 2gx + 2fy +c =0)$

$2ax+2h[x\frac{dy}{dx} +y] +2by\frac{dy}{dx} +2g +2f\frac{dy}{dx} +0=0$

On dividing both sides by 2, we get,

               $ax+h[x\frac{dy}{dx} +y] +by\frac{dy}{dx} +g +f\frac{dy}{dx} =0$

               $ax+hx\frac{dy}{dx} +hy +by\frac{dy}{dx} +g +f\frac{dy}{dx} =0$

                                       $hx\frac{dy}{dx} +by\frac{dy}{dx} +f\frac{dy}{dx} = -(ax+hy+g)$

                                            $(hx+by+f)\frac{dy}{dx}=-(ax+hy+g)$

Hence,

                                                                 $\frac{dy}{dx}=-\frac{(ax+hy+g)}{(hx+by+f)}$

This is the required derivative.