Consider the curve

MATHEMATICS · Single correct · AP · Calculus AB · Differentiation: Composite, Implicit, and Inverse Functions · Differentiation: Composite, Implicit, and Inverse Functions

Problem

Consider the curve x2+λy2=10yx^{2} + \lambda y^{2} = 10y. Determine λ\lambda if the tangent to the curve at the point (1,2)(1,2) is parallel to the line 2x+9y=02x + 9y = 0. (a) 4318\dfrac{43}{18} (b) 194\dfrac{19}{4} (c) 14\dfrac{1}{4} (d) 4718\dfrac{47}{18}

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