Given: circle O with diameter CD C(-5,4) D(3,-2) create a equation if the circle?

1 Answer
iceman
Apr 18, 2018

#(x+1)^2+(y-1)^2=25#

Explanation:

Mid point CD is the center:
The midpoint of a segment with endpoints A = (x₁, y₁) and B = (x₂, y₂) has coordinates :
[(x₁ + x₂) /2 , (y₁ + y₂)/2]
so in this case the center is:
#[(-5 + 3) /2 , (4 - 2)/2]# = #(-1, 1)#

Half of Length of CD is the radius:
distance 'd' between the points A = (x₁, y₁) and B = (x₂, y₂) is:
d = √[(x₂ - x₁)² + (y₂ - y₁)²]
so in this case:
#r = 1/2√[(3 + 5)^2 + (-2 - 4)^2]#
#r = 1/2 √[(8)^2 + (-6)^2]#
#r = 1/2√(64+36)=5#

The equation of the circle:
#(x+1)^2+(y-1)^2=25#

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