Equation of Circle


Videos and lessons with examples and solutions to help High School students derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation.

Related Topics:
Common Core Geometry
Common Core Mathematics




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Common Core: HSG-GPE.A.1

The following figure shows how to derive the equation of a circle. Scroll down the page for more examples and solutions.
Equation of a Circle
 

Equation For a Circle
This lesson shows two examples regarding how to find the equation of a circle centered at the origin.
Examples:

  1. Determine an equation for a circle with radius 3 units and centered at the origin.
  2. Determine an equation for the circle through the point (-3,4) with center at the origin.
  3. Check to see if each of the following points is on, inside or outside the circle for example 2.
    a) (2, -3)
    b) (1, 5)
    c) (-4, -3)

Completing the square to write equation in standard form of a circle
Example:
Graph the circle x2 + y2 + 4x - 4y - 17 = 0

Radius and center for a circle equation in standard form.
Example:
The equation of a circle C is (x + 3)2 + (y - 4)2 = 49
What is its center (h, k) and its radius r?




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