The curve passes through the point for certain values of the constant

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

Problem

The curve x2+y2+kxy=9x^2+y^2+kxy=9 passes through the point (1,2)(1,2) for certain values of the constant kk. For which value(s) of kk, if any, is the tangent line at (1,2)(1,2) horizontal? (a) k=−1k=-1 (b) k=−4k=-4 (c) No real value of kk results in a horizontal tangent at (1,2)(1,2) (d) k=2k=2

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