Answer:
(x + 5)² + (y – 1)² = 25
Explanation:
Note that the general equation of a circle is (x – h)² + (y – k)² = r², where (h, k) represents the location of the circle's center, and r represents the length of its radius.
The circle is 10 units in diamater, so the radius is half this: r=10/2=5.
The circle goes from -10 to 0 along the x-axis, so the x-coordinate of its centre is halfway between this: h=(-10+0)/2=-10/2=-5
The circle goes from -4 to 6 along the y-axis, so the y-coordinate of its centre is halfway between this: k=(-4+6)/2=-2/2=1
Now that we know r, h, and k, we can sub these into the general formula to get our equation:
(x - (-5))² + (y – 1)² = 5²
(x + 5)² + (y – 1)² = 25