The curve is cut by the vertical line at a point

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

Problem

The curve x2+λxy+y2=29x^{2} + \lambda xy + y^{2} = 29 is cut by the vertical line x=4x = 4 at a point (4,y1)(4,y_{1}). If the tangent to the curve at this point is perpendicular to the line y=xy = x, determine λ\lambda. (a) 316\dfrac{3}{16} (b) −38-\dfrac{3}{8} (c) −316-\dfrac{3}{16} (d) −163-\dfrac{16}{3}

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