Write the standard form of the equation of the circle with the given center and radius.
1. center (-2, 0) and r = 3
The standard form equation of a circle:
( x - h ) ^ 2 + ( y - k ) ^ 2 = r ^ 2
h are the x coordinate of the center of the circle.
k are the y coordinate of the center of the circle.
r = radius
In this case:
h = - 2
k = 0
r = 3
So equation of a circle :
( x + 2 ) ^ 2 + y ^ 2 = 9
To find the standard form of the equation of a circle given the center and radius, we use the formula:
(x - h)^2 + (y - k)^2 = r^2
where (h, k) represents the coordinates of the center and r represents the radius.
In this case, the center is (-2, 0), and the radius is 3. Plugging these values into the formula, we get:
(x - (-2))^2 + (y - 0)^2 = 3^2
Simplifying:
(x + 2)^2 + y^2 = 9
Therefore, the standard form of the equation of the circle with center (-2, 0) and radius 3 is (x + 2)^2 + y^2 = 9.