Write an equation of a circle with the given center and radius center (3,4) and radius 6.
The equation of a circle with center (a,b) and radius r is:
(x-a)^2 + (y-b)^2 = r^2
Substituting a=3, b=4, and r=6:
(x-3)^2 + (y-4)^2 = 6^2
Simplifying:
(x-3)^2 + (y-4)^2 = 36
Therefore, the equation of the circle with center (3,4) and radius 6 is (x-3)^2 + (y-4)^2 = 36.
To write the equation of a circle with a given center and radius, we can use the standard form equation of a circle:
(x - h)^2 + (y - k)^2 = r^2
Where (h, k) represents the center of the circle, and r represents the radius.
Given center (3, 4) and radius 6, we can substitute these values into the equation to get:
(x - 3)^2 + (y - 4)^2 = 6^2
Simplifying further, we have:
(x - 3)^2 + (y - 4)^2 = 36
Therefore, the equation of the circle with center (3, 4) and radius 6 is (x - 3)^2 + (y - 4)^2 = 36.