Question

A city plans to build a circular park around a historical site. The center of this park is located at (3,−2)
. If the park's radius is 7 units, representing the boundary in meters, what is the equation of the circular boundary?(1 point)
Responses

x2+y2=49
x squared plus y squared is equal to 49

(x−3)2+(y+2)2=7
open paren x minus 3 close paren squared plus open paren y plus 2 close paren squared is equal to 7

(x+3)2+(y−2)2=7
open paren x plus 3 close paren squared plus open paren y minus 2 close paren squared is equal to 7

(x−3)2+(y+2)2=49

Answer 1

To find the equation of the circular boundary of the park, we use the standard form of the equation of a circle:

\[
(x - h)^2 + (y - k)^2 = r^2
\]

where \((h, k)\) is the center of the circle and \(r\) is the radius.

In this case, the center of the park is at \((3, -2)\) (so \(h = 3\) and \(k = -2\)), and the radius is 7 units.

Now we calculate \(r^2\):

\[
r^2 = 7^2 = 49
\]

Substituting in the values for \(h\), \(k\), and \(r^2\) into the circle equation:

\[
(x - 3)^2 + (y + 2)^2 = 49
\]

Thus, the correct equation of the circular boundary is:

\[
\boxed{(x - 3)^2 + (y + 2)^2 = 49}
\]