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Circle Equation Calculator

Radius and Center
(h,k)=(,)
and r =
Diameter Points
A = (,)
B = (,)
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:

h = -1 * -2 = 2

Determine k:

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

General form of circle equation

Center (h, k) = (-2, +5) and r = r = 9:

Expand the standard form

x2 + y2 - 2hx - 2ky + h2 + k2 - r2 = 0

Plugg in our values for h,k, and r:

x2 + y2 - 2(-2)x - 2(+5)y + -22 + +52 - 92 = 0
x2 + y2 + 4x - 10y + 4 + 25 - 81 = 0

Combine our constants

x2 + y2 + 4x - 10y - 52 = 0

x2 + y2 + 4x - 10y - 52 = 0



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


What is the Answer?

x2 + y2 + 4x - 10y - 52 = 0

How does the Circle Equation Calculator work?

This calculates the standard equation of a circle and general 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)
This also allows you to enter a standard or general form equation so that the center (h,k) and radius r can be determined.
This calculator has 8 inputs.

What 1 formula is used for the Circle Equation Calculator?

  1. (x - h)2 + (y - k)2 = r2 where (h,k) is the center of the circle and r = radius.

For more math formulas, check out our Formula Dossier

What 8 concepts are covered in the Circle Equation Calculator?

center
circle
the set of all points in the plane that are a fixed distance from a fixed point
circle equation
An equation used to graph a circle
diameter
distance from two endpoints of a circle through the center
d = 2r
equation
a statement declaring two mathematical expressions are equal
midpoint
the middle point of a line segment. It is equidistant from both endpoints. It bisects the segment.
origin
On a two digit coordinate plane, the point (0, 0), where the x-axis and y-axis cross.
radius
Distance from the center of a circle to the edge
C/2π

Example calculations for the Circle Equation Calculator

  1. (1,1)(2,4)
  2. (1,4) and (5,6)
  3. (h,k) = (2,- 4) and r = 5
  4. (x - 2)^2 + (y + 5)^2 = 81

Circle Equation Calculator Video


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