Matlab the equation of a circle with its center at x=3 and y=2 is given by , where r is the radius of the circle. first derive the equation(symbolically) of the tangent line to the circle at the point on the upper part of the circle ( and ). then for specific values of r, , , make a plot of the circle and the tangent line. (r=9, )

The equation of a circle with center at (h,k) and radius r is

we are given
center is at (3,2)

solving for y



take the derivitive to find the slope at any point


we can use point slope form
for apoint (h,k) and slope m, the equation is
y-k=m(x-h)
not sure if you want in terms of what
I'll just say for a point (h,k)
so we get

where
that's the equation of the tangent line at (h,k) for arbitrary values of r

do the plots and other stuff yourself