Differentiation Question 168
Question: If $ ax^{2}+2hxy+by^{2}+2gx+2fy+c=0 $ , then $ \frac{dy}{dx}= $
Options:
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
Show Answer
Answer:
Correct Answer: A
Solution:
$ ax^{2}+2hxy+by^{2}+2gx+2fy+c=0 $
Differentiating w.r.t. x of y, we get $ 2ax+2h( y+x\frac{dy}{dx} )+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)} $ .
BETA
