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Give the equation for the new circle obtained by translating the circle (x+2)^2 + (y-1)^2 = 25 by 3 units to the right and 2 units down

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facundo3141592

Answer:

(x - 1)^2 + (y + 1)^2 = 25

Step-by-step 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

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