An ellipse has the equation

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

Problem

x^2 + xy + y^2 = 3

. The equation of the tangent at the point

P(1, 1)

can be written in the form

y = p + qx, \quad p, q \in \mathbb{Z}.

Find the values of

p

and

q

, giving your answer in the form

p, q

Related theory

Ellipse
Conic Sections
Advanced Differentiation
Implicit and parametric differentiation
Derivatives of implicit functions
Continuity and Differentiability

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