The family of circles depends on the non–zero real parameter .

MATHEMATICS · Multi-part · AP · Calculus AB · Differentiation: Composite, Implicit, and Inverse Functions · Differentiation: Composite, Implicit, and Inverse Functions

Problem

The family of circles x2+(y−b)2=b2x^2 + (y - b)^2 = b^2 depends on the non–zero real parameter bb. (i) Derive dydx\dfrac{dy}{dx} in terms of xx, yy and bb. (ii) Determine the values of bb for which at least one point on the circle has a tangent slope equal to 33. (iii) For each admissible value of bb, find the coordinates of all points where the tangent has slope 33.

Related theory

Browse the problem library