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.

**Related Topics**

**Equation of a circle****With center and radius****Equation of a circle passing though three points****Length of the tangent to a circle****Equation of the tangent to a circle****Family of circles****Orthogonal circles****Section formula****Area of triangle****Area of triangle worksheets****Area of quadrilateral****Centroid****Centroid of the triangle worksheets****Finding missing vertex using centroid worksheet****Midpoint****Distance between two points****Distance between two points worksheet****Slope of the line****Equation of the line****Equation of line using two points worksheet****Equation of the line using point and slope worksheets****Point of intersection of two lines****Point of intersection Worksheets****concurrency of straight line****Concurrency of straight lines worksheet****Circumcentre of a triangle****Circumcentre of Triangle Worksheet****Orthocentre of a triangle****Orthocentre of Triangle Worksheet****Incentre of a triangle****Locus****Perpendicular distance****Angle between two straight lines****Parabola****Ellipse**

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