Write an equation of a circle with the given center and radius.
center (-7, -6) and radius 2.
A. (x+7)^2+(y+6)^2=4
B. (x-7)^2+(y-6)^2=2
C. (x+7)^2+(y+6)^2=2
D. (x-7)^2+(y-6)^2=4
To write the equation of a circle, you need to know the center and the radius. The equation of a circle with center (h, k) and radius r is given by:
(x - h)^2 + (y - k)^2 = r^2
In this case, the center is (-7, -6) and the radius is 2. Plugging these values into the equation, we get:
(x - (-7))^2 + (y - (-6))^2 = 2^2
Simplifying, we have:
(x + 7)^2 + (y + 6)^2 = 4
So, the correct answer is A. (x+7)^2 + (y+6)^2 = 4.
The equation of a circle with center (h, k) and radius r is given by the standard form equation:
(x - h)^2 + (y - k)^2 = r^2
Given the center (-7, -6) and radius 2, we substitute the values into the standard form equation:
(x - (-7))^2 + (y - (-6))^2 = 2^2
Simplifying:
(x + 7)^2 + (y + 6)^2 = 4
Therefore, the equation of the circle with the given center and radius is: (x + 7)^2 + (y + 6)^2 = 4.
So the correct option is A. (x+7)^2+(y+6)^2=4.
general circle equation ... (x - h)^2 + (y - k)^2 = r^2
circle centered at (h,k), with radius r