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- x^2+y^2=1
- radius\:x^2-6x+8y+y^2=0
- center\:(x-2)^2+(y-3)^2=16
- area\:x^2+(y+3)^2=16
- circumference\:(x-4)^2+(y+2)^2=25
circle-function-calculator
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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?
- (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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