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.