Pidardo draws a circle on the coordinate plane. The circle has the equation 16 - (x + 2) *)

Question

16 - (x + 2)?) - 5. The circle is now
translated 3 units to the right and 3 units up. Where is the translated circle's center?
(1 point)

Answer 1

To find the center of the original circle given the equation \( 16 - (x + 2)^2 - (y - 5)^2 = 0 \), we can rewrite it in standard form.

Starting from the equation:

\[ 16 - (x + 2)^2 - (y - 5)^2 = 0 \]

We can rearrange it to the standard form of a circle:

\[ (x + 2)^2 + (y - 5)^2 = 16 \]

Here, we see that the center of the circle is at:

\[ (-2, 5) \]

Now, the circle is translated 3 units to the right and 3 units up.

• Translating 3 units to the right means adding 3 to the x-coordinate: \(-2 + 3 = 1\)

• Translating 3 units up means adding 3 to the y-coordinate: \(5 + 3 = 8\)

Thus, the new center of the translated circle is at:

\[ (1, 8) \]

Therefore, the center of the translated circle is \(\boxed{(1, 8)}\).