Answer:
[tex]\displaystyle (x-3)^2 + (y+2)^2 = 36[/tex]
Step-by-step explanation:
We want to write the equation of a circle with a center at (3, -2) and a radius of 6 units.
Recall that the equation of a circle is given by:
[tex]\displaystyle (x-h)^2 + (y-k)^2 = r^2[/tex]
Where (h, k) is the center and r is the radius.
Since our center is at (3, -2), h = 3 and k = -2. r = 6. Substitute:
[tex]\displaystyle (x-(3))^2 +(y-(-2))^2 = (6)^2[/tex]
Simplify:
[tex]\displaystyle (x-3)^2 + (y+2)^2 = 36[/tex]
In conclusion, the equation of the circle will be:
[tex]\displaystyle (x-3)^2 + (y+2)^2 = 36[/tex]
