The curves and intersect once in the first quadrant

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

Problem

The curves

x^{2}+y^{2}=10

and

xy=5

intersect once in the first quadrant. The equation of their common tangent at that point is (a)

x+y=2\sqrt{5}

(b)

x+y=\sqrt{10}

(c)

x-y=\sqrt{5}

(d)

y=x

Related theory

Theorems
Advanced Differentiation
Implicit and parametric differentiation
Derivatives of implicit functions
Continuity and Differentiability

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