# How do you find an equation of the circle that passes through the pts (0,0) and (1,1) and has its center on the line y=2?

##### 1 Answer

Jan 20, 2016

#### Answer:

#### Explanation:

If the center of the circle is on

then the center of the circle is at

The radius of the circle,

- The distance from
#(x_c,2)# to#(0,0)#

#color(white)("XXX")=sqrt((x_c-0)^2+(2-0)^2)=sqrt(x_c^2+4)# - The distance from
#(x_c,2)# to#(1,1)#

#color(white)("XXX")=sqrt((x_c-1)^2+(2-1)^2) = sqrt(x_c^2-2x_c+1+1)#

Therefore

and since

The general equation of a circle with center

By substituting

graph{(x+1)^2+(y-2)^2=5 [-5.8, 5.3, -0.764, 4.783]}