Calculator Instructions:

This calculates the equation of a circle from the following given items:

* A center (h,k) and a radius r

* A diameter A(a_{1},a_{2}) and B(b_{1},b_{2}) Related Formulas:

(x - h)^{2} + (y - k)^{2} = r^{2} where (h,k) is the center of the circle and r = radius. Search Engine Shortcut Examples:

(1,1)(2,4)

(1,4) and (5,6)

(h,k) = (2,- 4) and r = 5

(x - 2)^2 + (y + 5)^2 = 81 Excel Download for Premium Users Only Quizzes Available for Premium Users Only Unlimited Practice Problem Generator for Premium Users Only Flashcards for Premium Users Only

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:__

From the standard form of a circle, we have h = -1 * -2 = 2

__Determine k:__

From the standard form of a circle, we have 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**

__Determine the general form of the circle equation given center (h, k) = (-2, +5) and radius r = 9:__

Expanding the standard form, we get the general form of x^{2} + y^{2} - 2hx - 2ky + h^{2} + k^{2} - r^{2} = 0

__Plugging in our values for h,k, and r, we get:__

Expanding the standard form, we get the general form of 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

Combining our constants, we have our general form of a circle equation below:

**x**^{2} + y^{2} + 4x - 10y - 52 = 0

To see the diameter, circumference, and area of this circle, visit our calculator

This calculates the equation of a circle from the following given items:

* A center (h,k) and a radius r

* A diameter A(a

(x - h)

(1,1)(2,4)

(1,4) and (5,6)

(h,k) = (2,- 4) and r = 5

(x - 2)^2 + (y + 5)^2 = 81 Excel Download for Premium Users Only Quizzes Available for Premium Users Only Unlimited Practice Problem Generator for Premium Users Only Flashcards for Premium Users Only

Evaluate the circle equation (x - 2)

This circle equation is in standard form: (x - h)

From the standard form of a circle, we have h = -1 * -2 = 2

From the standard form of a circle, we have k = -1 * +5 = -5

Therefore, our circle has a center (h, k) = (2, -5)

Therefore, we have r

r = ±√81

Since a radius is always positive, we have r =

Expanding the standard form, we get the general form of x

Expanding the standard form, we get the general form of x

x

Combining our constants, we have our general form of a circle equation below:

To see the diameter, circumference, and area of this circle, visit our calculator