Question

The slope of the circle x^2+y^2=25 at the point (3,-4)

Answer 1

$y = \sqrt{25 - {x}^{2} } \\ \frac{dy}{dx} = \frac{1}{2 \sqrt{25 - {x}^{2} } } ( - 2x) \\ slope = \frac{ - x}{ \sqrt{25 - {x}^{2} } } \\ at \: x = 3 \: y = - 4 \\ \\ slope = \frac{ - 3}{3} = - 1$

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