Let the curve be defined by and consider the point .

MATHEMATICS · Multi-part · AP · Calculus AB · Differentiation: Composite, Implicit, and Inverse Functions · Differentiation: Composite, Implicit, and Inverse Functions

Problem

Let the curve be defined by x2+xy+y2=7x^{2}+xy+y^{2}=7 and consider the point R(1,2)R(1,2). (1) Confirm that RR lies on the curve. (2) Compute dydx\dfrac{dy}{dx} at RR. (3) Express the tangent line at RR in parametric form with parameter tt, choosing t=0t=0 to correspond to the point RR. Provide both x(t)x(t) and y(t)y(t). (For example, you may write x(t)=…x(t)=\ldots and y(t)=…y(t)=\ldots.)

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