# How do you write the equation of the circle whose diameter goes from A(7,-2) to B(1,12)?

##### 1 Answer

#### Explanation:

The general equation for a circle is:

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

where

The center of the circle will be the midpoint of the endpoints of the diameter. The midpoint formula is as follows:

#((x_1+x_2)/2,(y_1+y_2)/2)#

Hence the midpoint:

#((7+1)/2,(-2+12)/2)=(4,5)#

The remaining piece of information we need is the radius, which can be found through finding the distance from the center point to either one of the diameter's endpoints, which lie on the circle. First, the distance formula:

#d=sqrt((x_1-x_2)^2+(y_1-y_2)^2)#

I'll choose

#d=sqrt((4-1)^2+(12-5)^2)#

#=sqrt(9+49)#

#=sqrt58#

The radius has length

Relate the center

#(x-4)^2+(y-5)^2=(sqrt58)^2#

#=>(x-4)^2+(y-5)^2=58#

graph{(x-4)^2+(y-5)^2=58 [-13.06, 22.99, -3.42, 14.6]}