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
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- 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
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- 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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Equation of a Circle Calculator is a free online tool that displays the equation of a circle of a given input. BYJU’S online equation of a circle calculator tool makes the calculation faster, and it displays the equation in a fraction of seconds.
How to Use the Equation of a Circle Calculator?
The procedure to use the equation of a circle calculator is as follows:
Step 1: Enter the circle centre and radius in the respective input
field
Step 2: Now click the button “Find Equation of Circle” to get the equation
Step 3: Finally, the equation of a circle of a given input will be displayed in the new window
What is the Equation of a Circle?
In geometry, a circle is a two-dimensional round shaped figure where all the points on the surface of the circle are equidistant from the centre point (c). The distance from the centre of the circle to the surface is called the radius (R). The equation
of a circle can be calculated if the centre and the radius are known. Thus the equation of a circle is given by
(x-h)2 +(y-k)2 = r2
Where
(h, k) – centre coordinates
r – radius