Ximpledu

Equation of a Circle

See how to write and use the equation of a circle.
6 examples and their solutions.

Equation of a Circle

Formula


(x - h)2 + (y - k)2 = r2

Example

Center: (2, 1), Radius: 3
Equation of the circle?
Solution

Example

Center: (4, 0), Diameter: 14
Equation of the circle?
Solution

Example

Endpoints of the diameter: (-1, 3), (7, 1)
Equation of the circle?
Solution

Example

x2 + y2 - 4x + 10y + 20 = 0
Center, r = ?
Solution

Equation of a Tangent: Circle

Formula


x1x + y1y = r2

Example

Write an equation of the line
tangent to the circle x2 + y2 = 10 at (3, 1).
Solution

System of Equations: Circle, Line

Example

x2 + y2 = 25
y = x + 1
Solution