In this page endpoints of diameter we are going to example problems to find the equation of a circle.
Example 1:
Find the equation of a circle if (2,-1) and (5,-3) are the endpoints of the diameter.
Solution:
Now we have to consider the given points as (x₁,y₁) and (x₂,y₂). So the values of x₁ = 2,y₁ = -1,x₂ = 5 and y₂ = -3
Formula to find the equation of circle if two endpoints of a diameter are given.
(x-x₁) (x-x₂) + (y-y₁) (y-y₂) = 0
( x - 2) (x - 5) + (y - (-1)) (y - (-3)) = 0
( x - 2) (x - 5) + (y + 1)) (y + 3)) = 0
x² - 2x - 5x + 10 + y² +y +3y + 3 = 0
x² - 7x + 10 + y² +4y + 3 = 0
x² - 7x + y² +4y + 10 + 3 = 0
x² - 7x + y² +4y + 13 = 0
So the required equation of a circle x² - 7x + y² +4y + 13 = 0.endpoints of diameter
Example 2:
Find the equation of a circle if (1,3) and (2,0) are the endpoints of the diameter.
Solution:
Now we have to consider the given points as (x₁,y₁) and (x₂,y₂). So the values of x₁ = 1,y₁ = 3,x₂ = 2 and y₂ = 0
Formula to find the equation of circle if two endpoints of a diameter are given.
(x-x₁) (x-x₂) + (y-y₁) (y-y₂) = 0
( x - 1) (x - 2) + (y - 3) (y - 0) = 0
( x - 1) (x - 2) + (y - 3) y = 0
x² - 2x - x + 2 + y² - 3y = 0
x² - 3x + y² - 3y + 2 = 0
So the required equation of a circle x² - 3x + y² - 3y + 2 = 0.
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