Find the equation of a circle with
Diameter endpoints = A(-4,5) and B(7,-3)
Step 1: Find the Midpoint (h,k) of AB:
| h = | A1 + B1 |
| 2 |
| h = | -4 + 7 |
| 2 |
| h = | 3 |
| 2 |
h = 1.5
| k = | A2 + B2 |
| 2 |
| k = | 5 + -3 |
| 2 |
| k = | 2 |
| 2 |
k = 1
Center of our circle is (h, k) = (1.5, 1)
Calculate radius:
r = Square Root((x2 - x1)2 + (y2 - y1)2)r = Square Root((7 - -4)2 + (-3 - 5)2)
r = ½Square Root((112 + -82))
r = ½√(121 + 64)
r = ½√185
r = ½(13.601470508735)
r = 6.8007
Find circle equation
Find the equation of the circle withcenter (h,k) = (1.5,1) and radius r = 6.8007
Standard Circle Equation:
(x - h)2 + (y - k)2 = r2Plugging in our numbers, we get:
(x - 1.5)2 + (y - 1)2 = 6.80072(x - 1.5)2 + (y - 1)2 = 46.24952049
General form of circle equation
Center (h, k) = (1.5, 1) and r = r = 6.8007:Expand the standard form
x2 + y2 - 2hx - 2ky + h2 + k2 - r2 = 0Plugg in our values for h,k, and r:
x2 + y2 - 2(1.5)x - 2(1)y + 1.52 + 12 - 6.80072 = 0x2 + y2 - 3x - 2y + 2.25 + 1 - 46.24952049 = 0
Combine our constants
x2 + y2 - 3x - 2y - 42.99952049 = 0x2 + y2 - 3x - 2y - 42.99952049 = 0
What is the Answer?
x2 + y2 - 3x - 2y - 42.99952049 = 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.
* 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
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
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