Radius of the circle: ((X-4)^2)+((y+2)^2)-81=0

Radius = 9

thanx

To find the radius of a circle, you need to rewrite the equation of the circle in the standard form. The standard form equation of a circle is (x - h)^2 + (y - k)^2 = r^2, where (h, k) represents the coordinates of the center of the circle, and r represents the radius.

Let's rewrite the given equation in standard form:

((x - 4)^2) + ((y + 2)^2) - 81 = 0

First, move the constant term (-81) to the right side:

((x - 4)^2) + ((y + 2)^2) = 81

Now, we can compare this equation to the standard form equation:

(x - h)^2 + (y - k)^2 = r^2

From the comparison, we can see that the center of the circle is the point (4, -2) since the equation is centered around (x - 4) and (y + 2).

The radius of the circle is the square root of the right side of the equation, which is 81:

r = √81

r = 9

Therefore, the radius of the given circle is 9 units.