Evaluate the circle equation:
(x - 2)
2 + (y + 5)
2 = 81
This circle equation is in standard form:
(x - h)
2 + (y - k)
2 = r
2 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 r
2 = 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 x
2 + y
2 - 2
h x - 2
k y +
h 2 +
k 2 -
r 2 = 0
Plugg in our values for h,k, and r: x
2 + y
2 - 2(
-2 )x - 2(
+5 )y +
-2 2 +
+5 2 -
9 2 = 0
x
2 + y
2 + 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
Common Core State Standards In This Lesson
What is the Answer?
x2 + y2 + 4x - 10y - 52 = 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 = r
2 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
Play
Tags: Add This Calculator To Your Website