# How to find the slope of the curve at the given point: x^2 + y^2 = 25 ; (3,-4) ?

The gradient in $\left(3 , - 4\right)$ is $\left(6 , - 8\right)$ so we can use the implicit function theorem and locally $y = f \left(x\right)$ and $f ' \left(x\right) = - {F}_{x} / {F}_{y} = - \frac{2 x}{2 y} = \frac{3}{4}$