Circle Equation Calculator

  Calculator Instructions:

This calculates the equation of a circle from the following given items:
* A center (h,k) and a radius r
* A diameter A(a1,a2) and B(b1,b2)
  Related Formulas:

(x - h)2 + (y - k)2 = r2 where (h,k) is the center of the circle and r = radius.
  Search Engine Shortcut Examples:

(1,1)(2,4)
(1,4) and (5,6)
(h,k) = (2,- 4) and r = 5
(x - 2)^2 + (y + 5)^2 = 81
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Circle Equation using (h,k) and radius (h,k)=(,) and r =
Diameter Points A = (,) and B = (,)
Enter Circle Equation
  

Evaluate the circle equation (x - 2)2 + (y + 5)2 = 81

This circle equation is in standard form: (x - h)2 + (y - k)2 = r2

Determine h:
From the standard form of a circle, we have h = -1 * -2 = 2

Determine k:
From the standard form of a circle, we have k = -1 * +5 = -5

Determine center of the circle:
Therefore, our circle has a center (h, k) = (2, -5)

Determine radius:
Therefore, we have r2 = 81
r = ±√81
Since a radius is always positive, we have r = 9

Determine the general form of the circle equation given center (h, k) = (-2, +5) and radius r = 9:
Expanding the standard form, we get the general form of x2 + y2 - 2hx - 2ky + h2 + k2 - r2 = 0

Plugging in our values for h,k, and r, we get:
Expanding the standard form, we get the general form of x2 + y2 - 2(-2)x - 2(+5)y + -22 + +52 - 92 = 0
x2 + y2 + 4x - 10y + 4 + 25 - 81 = 0
Combining our constants, we have our general form of a circle equation below:
x2 + y2 + 4x - 10y - 52 = 0

To see the diameter, circumference, and area of this circle, visit our calculator