for the curve x^2+z^2+2gx+2hy=0 value of dy/dx at(0,0) is

Question

A. -g/h
B. g/h
C. h/g
D. None

Please help me.
In the answer page it shows option A as answer. I don't know deeply of differentiation . Please could you help me by explain how the answer is A

Answer 1

x^2+y^2+2gx+2hy=0
2x + 2yy' + 2g + 2hy' = 0
y'(y+h) = -(x+g)
y' = -(x+g)/(y+h)
at (0,0) y' = -g/h

or

x^2+y^2+2gx+2hy=0
(x+g)^2 + (y+h)^2 = g^2+h^2
2(x+g) + 2(y+h) y' = 0
y' = -(x+g)/(y+h)

Answer 2

Thanks Sir

Answer 3

Tnx sir this helped a lot