Question

What is the slope for the line tangent to the circle x2 + y2 = 8 at the point (2, -2)?

Answer 1

slope = dy/dx at point (2,-2)
differentiate circle equation and solve for dy/dx
\[\rightarrow 2x +2y \frac{dy}{dx} = 0\]
\[\rightarrow \frac{dy}{dx} = -\frac{x}{y}\]
plug in point
\[\frac{dy}{dx} = \frac{-2}{-2} = 1\]