center (h,k) = (2,-4) and radius r = 5
Standard Circle Equation:
(x - h)2 + (y - k)2 = r2Plugging 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 = 0Plugg in our values for h,k, and r:
x2 + y2 - 2(2)x - 2(-4)y + 22 + -42 - 52 = 0x2 + y2 - 4x + 8y + 4 + 16 - 25 = 0
Combine our constants
x2 + y2 - 4x + 8y - 5 = 0x2 + y2 - 4x + 8y - 5 = 0
Common Core State Standards In This Lesson
HSG.GPE.A.1
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.
* 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.
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
