Discussion
For the circle \( x^{2} + y^{2} = 25 \), the slope \( dy/dx \) at the point \( (3, 4) \) is
Answer: B
Differentiate implicitly and solve for the slope:
\[ 2x + 2y\,\frac{dy}{dx} \;=\; 0 \quad \Longrightarrow \quad \frac{dy}{dx} \;=\; -\frac{x}{y}. \]
At \( (3,4) \) this is \( -3/4 \). The tangent is perpendicular to the radius, whose slope is \( 4/3 \), and the product of the two slopes is \( -1 \) as it must be
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