Question

Write the equation of the circle R that passes through (1, 1) and has a center C(2, 2).

Answer 1

$(x-x_0)^2+(y-y_0)^=r^2 (x-2)^2+(y-2)^=2$Firstly, we need to find out the radius of the circle

and this is accomplished by the distance formula$r=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2} \\ r=\sqrt{(2-1)^2+(2-1)^2} \\ r=\sqrt{1+1} \\ r=\sqrt{2} hence:\\ \\ r^2=2$

then the equation of the circle is:

$(x-x_0)^2+(y-y_0)^2=r^2\\ \\(x-2)^2+(y-2)^2=2$