Question 877742
Find the radius by using the distance between the center and the point.
{{{R^2=(2-5)^2+(15-15)^2}}}
{{{R^2=(-3)^2}}}
{{{R=3}}}
.
.
{{{(x-2)^2+(y-15)^2=9}}}
Take the derivative to find the slope of the tangent line at any point,
{{{2(x-2)+2(y-15)=0}}}
{{{(2x-4)dx+(2y-30)dy=0}}}
{{{(2y-30)dy=(4-2x)dx}}}
{{{dy/dx=(4-2x)/(2y-30)}}}
{{{m=dy/dx=(2-x)/(y-15)}}}
At {{{x=5}}},
{{{m=(2-5)/(15-15)}}}
The slope is infinite at that point.
{{{x=5}}} is the tangent.
{{{drawing(300,300,-5,15,-2,18,grid(1),
circle(2,15,3),circle(2,15,0.3),
circle(5,15,0.3),green(line(2,15,5,15)),blue(line(5,-100,5,100)))}}}