Consider the family of curves defined by

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

Problem

Consider the family of curves defined by x2+kxy+y2=1x^{2}+kxy+y^{2}=1, where kk is a constant parameter. Which of the following gives dydx\dfrac{dy}{dx} expressed in terms of xx, yy, and kk? (a) 2x+kykx+2y\dfrac{2x+ky}{kx+2y} (b) −2x+kykx+2y-\dfrac{2x+ky}{kx+2y} (c) −kx+2y2x+ky-\dfrac{kx+2y}{2x+ky} (d) −2x+ky2y-\dfrac{2x+ky}{2y}

Related theory

Browse the problem library