Circle Equation Calculator

Radius and Center (h,k)=(,) and r =
Diameter Points A = (,) B = (,)
Circle Equation

  

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Find the equation of the circle with
center (h,k) = (2,-4) and radius r = 5

Standard Circle Equation:

(x - h)² + (y - k)² = r²

Plugging 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 = 0

Plugg in our values for h,k, and r:

x² + y² - 2(2)x - 2(-4)y + 2² + -4² - 5² = 0
x² + y² - 4x + 8y + 4 + 16 - 25 = 0

Combine our constants

x² + y² - 4x + 8y - 5 = 0