identify the center and radius of the circle with the equation
(x+5)^2+(y-2)^2=9
A. this equation represents a circle with center (5,-2) and a radius of 3 units
B. This equation represents a circle with center (-5,2) and a radius of 3 units
C. this equation represents a circle with center (5,-2) and a radius of 9 units
d. this equation represents a circle with center (-5,2) and a radius of 9 units
C(h,k), P(x,y).
x - h = x+5
x-x-h = 5
-h = 5
h = -5
y-k = y-2
y-y-k = -2
-k = -2
k = 2
C(-5,2).
r = sqrt(9) = 3 Units.
To identify the center and radius of the given circle equation, we can compare it to the standard form equation of a circle, which is:
(x - h)^2 + (y - k)^2 = r^2
Where (h, k) represents the center of the circle and r represents the radius.
In the given equation: (x+5)^2 + (y-2)^2 = 9
We can see that h = -5, k = 2, and r^2 = 9.
Therefore, the center of the circle is (-5, 2), and the radius of the circle is the square root of 9, which is 3 units.
So, the correct answer is option B. This equation represents a circle with center (-5, 2) and a radius of 3 units.