Mathematics

Mathematics

Problem

For a polar curve given by r=f(θ)r = f(\theta) with r≠0r\ne 0, which of the following sets of conditions guarantees that the tangent line to the curve at angle θ\theta is vertical? a) dydθ=0 and dxdθ≠0\dfrac{dy}{d\theta}=0 \text{ and } \dfrac{dx}{d\theta}\ne 0 b) dxdθ=0 and dydθ≠0\dfrac{dx}{d\theta}=0 \text{ and } \dfrac{dy}{d\theta}\ne 0 c) dydx=0\dfrac{dy}{dx}=0 d) dxdθ=0 and dydθ=0\dfrac{dx}{d\theta}=0 \text{ and } \dfrac{dy}{d\theta}=0

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