For the curve

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

Problem

For the curve x2y+y2=10x^2 y + y^2 = 10, let (1,y1)(1,y_1) be the point on the curve with y1>0y_1>0. The normal to the curve at this point meets the yy-axis at (a) 2141−1\dfrac{21}{\sqrt{41}-1} (b) 21−24141−1\dfrac{21 - 2\sqrt{41}}{\sqrt{41} - 1} (c) 21−24141+1\dfrac{21 - 2\sqrt{41}}{\sqrt{41}+1} (d) 43−341241\dfrac{43 - 3\sqrt{41}}{2\sqrt{41}}

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