AP Calculus ABeasymcq1 pt

The curve x2+y2=25x^2+y^2=25 passes through the point (3,4)(3,4). An equation of the tangent line to the curve at this point is

A.y4=43(x3)y-4=\dfrac{4}{3}(x-3)
B.y4=43(x3)y-4=-\dfrac{4}{3}(x-3)
C.y4=34(x3)y-4=-\dfrac{3}{4}(x-3)
D.y4=34(x3)y-4=\dfrac{3}{4}(x-3)

Explanation

Core Concept

Implicit differentiation gives dydx=xy=34\frac{dy}{dx}=-\frac{x}{y}=-\frac{3}{4} at (3,4)(3,4). Point-slope form then gives y4=34(x3)y-4=-\frac{3}{4}(x-3).

Correct Answer

Cy4=34(x3)y-4=-\dfrac{3}{4}(x-3)

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