for the curve x^2+z^2+2gx+2hy=0 value of dy/dx at(0,0) is
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
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)
Thanks Sir
Tnx sir this helped a lot
To find the value of dy/dx at the point (0,0) for the given curve, you first need to differentiate the equation with respect to x.
The given equation is x^2 + z^2 + 2gx + 2hy = 0.
Differentiating both sides with respect to x, we get:
2x + 2g + (2h)(dy/dx) = 0.
Now, we can isolate dy/dx, which represents the slope of the curve at the point (0,0):
(2h)(dy/dx) = -2x - 2g.
Dividing both sides by 2h:
dy/dx = (-2x - 2g) / (2h).
At the point (0,0), x = 0, so the equation becomes:
dy/dx = (-2(0) - 2g) / (2h),
dy/dx = -2g / (2h),
Simplifying further:
dy/dx = -g / h.
Thus, the correct answer is option A: -g/h.