Answer to Question #90666 in Geometry for Yaya

Question

Suppose AB is the diameter of a circle, where A =(-1,1) and B = (-4,-5). What is the equation of the circle?

Answer 1

The center-radius form of the circle equation is in the format (x-a)²+(x-b)²=r², with the center being at the point O(a, b) and the radius being "r ". If AB is the diameter of a circle, where A =(-1,1) and B = (-4,-5), then the center O(a, b) is a midpoint of AB.

a=(-1+(-4))/2=-2.5, b=(1+(-5))/2=-2, then the center is O(-2.5,-2). 

r=AB/2

r²=AB²/4

AB²= (-4-(-1))²+(-5-1)²=(-5)²+(-6)=25+36=61

 r²=61/4=15.25

r²=15.25

(x-(-2.5))²+(y-(-2))²=15.25

The equation of the circle is (x+2.5)²+(y+2)²=15.25