Equation of a circle calculator given center and point

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Find the equation of a circle that has a diameter with the endpoints given by the points A(1,1) and B(2,4)

Step 1: Find the Midpoint (h,k) of AB:

h = 1.5

k = 2.5
From above, the center of our circle is (h, k) = (1.5, 2.5)

Calculate radius:

r = Square Root((x2 - x1)2 + (y2 - y1)2)
r = Square Root((2 - 1)2 + (4 - 1)2)
r = ½Square Root((12 + 32))
r = ½√(1 + 9)
r = ½√10
r = ½(3.1622776601684)
r = 1.5811

Now calculate our circle equation using (h, k), and r

Find the equation of the circle with center (h,k) = (1.5,2.5) and radius r = 1.5811
The standard equation for a circle is (x - h)2 + (y - k)2 = r2

Plugging in our numbers, we get:

(x - 1.5)2 + (y - 2.5)2 = 1.58112
(x - 1.5)2 + (y - 2.5)2 = 2.49987721

Determine the general form of the circle equation given center (h, k) = (1.5, 2.5) and radius r = 1.5811:

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(1.5)x - 2(2.5)y + 1.52 + 2.52 - 1.58112 = 0
x2 + y2 - 3x - 5y + 2.25 + 6.25 - 2.49987721 = 0

Combining our constants, we have our general form of a circle equation below:

x2 + y2 - 3x - 5y + 6.00012279 = 0

x2 + y2 - 3x - 5y + 6.00012279 = 0

What is the Answer?

x2 + y2 - 3x - 5y + 6.00012279 = 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?

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

What other resources can help with the Circle Equation Calculator?

Circle Equation Calculator Video

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