# How do you find the equation of a circle with points (1, 2) and (–1, –2) as endpoints of a diameter?

##### 1 Answer

Nov 25, 2016

#x^2+y^2=5#

#### Explanation:

The circle is passing through the points

This is the diameter of the circle. Its midpoint is the center of the circle and half of the diameter is the radius of the circle.

Mid - point / center of the circle

#(x, y)= (x_1+x_2)/2, (y_1+y_2)/2#

#(x, y)= (-1+1)/2, (-2+2)/2 = (0, 0)#

Center of the circle is

Its radius is the distance between

#r=sqrt[(x_1-x_2)+(y_1-y_2)]#

#r=sqrt[(0-(-1))+(0-(-2))#

#r=sqrt(1+4)=sqrt5#

The equation of the circle having

#x^2+y^2=r^2#

in our case -

#r=sqrt5#

Then -

#r=5#

Hence the required equation is -

#x^2+y^2=5#