Question

Let x2 + y2 = 122y.

First find
dy
dx
by implicit differentiation, simplifying the answer where reasonable. Then find an equation of the line L tangent to the graph of the given equation at the point (11, 1).

Answer 1

x^2 + y^2 = 122y
2x + 2yy' = 122y'
y' = 2x/(122-2y) = x/(61-y)
at (11,1), y' = 11/60
so the line required is
y-1 = 11/60 (x-11)