For the curve given by and

MATHEMATICS · Single correct · AP · Calculus BC · Parametric, Polar, and Vector-Valued Functions · Parametric, Polar, and Vector-Valued Functions

Problem

For the curve given by x=acos⁡t+bsin⁡tx=a\cos t+b\sin t and y=asin⁡t−bcos⁡t  (a≠0, b≠0)y=a\sin t-b\cos t\;(a\neq 0,\,b\neq 0), the value of d2ydx2\dfrac{d^{2}y}{dx^{2}} at t=0t=0 is (a) a2+b2a3\dfrac{a^{2}+b^{2}}{a^{3}} (b) a2+b2b3\dfrac{a^{2}+b^{2}}{b^{3}} (c) a2−b2b3\dfrac{a^{2}-b^{2}}{b^{3}} (d) a2+b2b4\dfrac{a^{2}+b^{2}}{b^{4}}

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