Endpoints Of Diameter

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

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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

Endpoints Of Diameter to Analytical Geometry