Circle Equation Calculator

June 14, 2024

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Circle Equation Calculator Image to Crop

Find the equation of the circle with
center (h,k) = (2,-4) and radius r = 5

Standard Circle Equation:

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

Plugging in our numbers, we get:

(x - 2)2 + (y - (-4))2 = 52
(x - 2)2 + (y + 4)2 = 25

General form of circle equation

Center (h, k) = (2, -4) and r = r = 5:

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(-4)y + 22 + -42 - 52 = 0
x2 + y2 - 4x + 8y + 4 + 16 - 25 = 0

Combine our constants

x2 + y2 - 4x + 8y - 5 = 0

You have 1 free calculations remaining

What is the Answer?

x2 + y2 - 4x + 8y - 5 = 0

How does the Circle Equation Calculator work?

Free Circle Equation Calculator - 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?

(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?

centercirclethe set of all points in the plane that are a fixed distance from a fixed pointcircle equationAn equation used to graph a circlediameterdistance from two endpoints of a circle through the center
d = 2requationa statement declaring two mathematical expressions are equalmidpointthe middle point of a line segment. It is equidistant from both endpoints. It bisects the segment.originOn a two digit coordinate plane, the point (0, 0), where the x-axis and y-axis cross.radiusDistance from the center of a circle to the edge
C/2π