Answer:
(x - 1)^2 + (y + 1)^2 = 25
Explanation:
The equation of a circle centered in the point (a, b) with a radius R is:
(x - a)^2 + (y - b)^2 = R^2
If we translate the circle 3 units to the right and 2 units down, then we translate the center 3 units to the right and 2 units down.
So if the original center was (a, b), and we translate it 3 units to the right, then we need to add 3 to the x-component, we get:
(a + 3, b)
Now if we want to move the center two units down, we need to subtract 2 in the y-value, we get:
(a + 3, b - 2)
This will be the new center of the circle.
Now let's look at our circle, we have:
(x + 2)^2 + (y - 1)^2 = 25
The center of this circle is:
(-2, 1)
After the translation, the center will be:
(-2 + 3, 1 - 2)
(1, -1)
Then the equation for the translated circle is:
(x - 1)^2 + (y - (- 1))^2 = 25
(x - 1)^2 + (y + 1)^2 = 25