A) \[-\frac{ax+hy+g}{hx-by+f}\]
B) \[\frac{ax+hy+g}{hx-by+f}\]
C) \[\frac{ax-hy-g}{hx-by-f}\]
D) None of these
Correct Answer: A
Solution :
\[a{{x}^{2}}+2hxy+b{{y}^{2}}+2gx+2fy+c=0\] Differentiating w.r.t. x of y, we get \[2ax+2h\left( y+x\frac{dy}{dx} \right)+2by\frac{dy}{dx}+2g+2f\frac{dy}{dx}=0\] \[\therefore \frac{dy}{dx}(2hx+2by+2f)=-(2ax+2hy+2g)\] or \[\frac{dy}{dx}=-\frac{(ax+hy+g)}{(hx+by+f)}\].You need to login to perform this action.
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