Equation Of a Circle Test

The standard form of the equation of a circle is given by: $$(x - h)^2 + (y - k)^2 = r^2$$ , where (h, k) is the center of the circle and r is the radius.

To find the center of a circle from its equation in standard form $$(x - h)^2 + (y - k)^2 = r^2$$ , identify the values of h and k. The center is (h, k).

The radius of the circle is the square root of r^2, which is r.

To convert from general form $$Ax^2 + Ay^2 + Bx + Cy + D = 0$$ to standard form, complete the square for the x and y terms.

The center of the circle is (-3, 2).

The radius of the circle is 5, since $$r^2 = 25$$ .

Use the formula $$(x - h)^2 + (y - k)^2 = r^2$$ , where (h, k) is the center and r is the distance from the center to the point.

The center is (-3, 6) and the radius is 5.

Completing the square is a method used to rewrite a quadratic equation in the form of a perfect square trinomial, which helps in converting to standard form.

The equation is $$(x - 2)^2 + (y + 3)^2 = 16$$ .