For the curve :

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

Problem

For the curve x2+xy+y2=7x^{2}+xy+y^{2}=7: (i) Verify that the point (1,2)(1,2) lies on the curve. (ii) Find the slope of the tangent to the curve at (1,2)(1,2). (iii) Hence obtain the equations of the tangent and the normal at the point (1,2)(1,2) in slope–intercept form.

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