Question 841415
Complete the square in x and y to get into standard form.
{{{(x-h)^2+(y-k)^2=R^2}}}
{{{x^2+10x+y^2-18y=-102}}}
{{{(x^2+10x+25)+(y^2-18y+81)=-102+25+81}}}
{{{(x+5)^2+(y-9)^2=4}}}
a) Center (h,k)=(-5,9)
b) Radius R=2
c) y intercepts : {{{x=0}}}
{{{25+(y-9)^2=4}}}
{{{(y-9)^2=-21}}}
Since no squared number can be negative, there are no y-intercepts (the circle doesn't cross the y-axis).
x intercepts : 
{{{(x+5)^2+81=4}}}
{{{(x+5)^2=-77}}}
Similarly, it doesn't cross the x-axis.
{{{drawing(300,300,-12,2,-2,12,grid(1),circle(-5,9,2), circle(-5,9,0.1))}}}