Mathematics

Problem

The family of circles

x^2 + (y - b)^2 = b^2

depends on the non–zero real parameter

b

. a. (i) Derive

\dfrac{dy}{dx}

in terms of

x

y

and

b

. b. (ii) Determine the values of

b

for which at least one point on the circle has a tangent slope equal to

3

. c. (iii) For each admissible value of

b

, find the coordinates of all points where the tangent has slope

3