find the points on x^2+y^2=11 where the tangent line has slope 11/60
at (x,y) on the circle, the slope is -y/x
So, -y/x = 11/60
y = -11x/60
x^2(1+121/3600) = 11
x^2 = 39600/3721
y^2 = 1331/3721
So, -y/x = 11/60
y = -11x/60
x^2(1+121/3600) = 11
x^2 = 39600/3721
y^2 = 1331/3721