Part 1Determine the center and radius of the circle described by the equation.left parenthesis x plus 3 right parenthesis squared plus left parenthesis y minus 2 right parenthesis squared equals 25(x+3)2+(y−2)2=25 Part 1centerequals=[input]enter your response here (Type your answer as an ordered pair.)

Question

Part 1Determine the center and radius of the circle described by the equation.left parenthesis x plus 3 right parenthesis squared plus left parenthesis y minus 2 right parenthesis squared equals 25(x+3)2+(y−2)2=25 Part 1centerequals=[input]enter your response here ​(Type your answer as an ordered​ pair.)

BlackTom AI · Accepted Answer

The equation given is already in the standard form for a circle: (x - h)^2 + (y - k)^2 = r^2. Here, we have (x + 3)^2 + (y - 2)^2 = 25.

To match the standard form, note that (x + 3)^2 is the same as (x - (-3))^2, so the center's x-coordinate h is -3. Likewise, (y - 2)^2 shows the center's y-coordinate k is 2. The right-hand side, 25, is r^2, so the radius r is the square root of 25, which is 5.

Therefore, the center of the circle is (-3, 2) and the radius is 5. Since the prompt asks for the center as an ordered pair, the appropriate entry is (-3, 2). In the provided input format, the first blank corresponds to the x-coordinate (-3), and the second blank corresponds to the y-coordinate (2).

If you were asked for the radius as well, you would report 5, since r = 5. The reasoning hinges on recognizing the circle standard form and extracting h, k, and r directly from the equation.

Homework:Module 9 Homework (Distance, Midpoint, Circles)

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