Question

Find an equation of the circle that has center (5, -1) and passes through (1, -5).

Answer 1

first, we need to find the radio r

r is the distance between the point and the center

$r=\sqrt[]{(x_1-x_2)^2+(y_1-y_2)^2}$

(5,-1)=(x1,y1)

(1,-5)=(x2,y2)

$r=\sqrt[]{(5-1)^2+(-1+5)^2}=\sqrt[]{4^2+4^2}=\sqrt[]{16+16}=\sqrt[]{32}=4\sqrt[]{2}$

r=5.66

the formula of the circle is

$(x-h)^2+(y-k)^2=r^2$

the center is (h,k)

in this case

h=5

k=-1

$(x-5)^2+(y+1)^2=(4\sqrt[]{2})^2=32$

the equation of the circle is

$(x-5)^2+(y+1)^2=32$