A circular sports field has equation ( 𝑥 − 4)2 + ( 𝑦 + 1)2 = 25. A ball lands at point (7,3). Determine whether the ball is inside, on, or outside the field.

A circular fountain is built at the center of a park located at coordinate (0,0). The water sprays up to 6 meters in all directions. Write the equation of the fountain’s boundary.

A robot operates within a circular boundary centered at (2,3) with radius 5 meters. The robot is currently at (6,6). Is it inside, on, or outside the boundary?

A radar system covers a circular area described by 𝑥2 + 𝑦2 − 6𝑥 + 8𝑦 − 11 = 0. An aircraft is located at point (1, –2). Determine whether the aircraft is inside, on, or outside the radar coverage.

A circular playground has its center at (4, –3) and radius 7 meters. Write the equation of the circle in standard form and then express it in general form.

A circular fountain satisfies: 𝑥2 + 𝑦2 − 10𝑥 − 14𝑦 + 65 = 0. Rewrite in standard form. Find the center and radius.

A circular restricted area is centered at (0,0) with radius 10 meters. A person stands at point (6,8). Determine whether the person is inside, on, or outside the restricted area.

An art installation has equation 𝑥2 + 𝑦2 + 4𝑥 − 10𝑦 − 20 = 0. A visitor is standing at point (3, 1). Determine whether the visitor is inside, on, or outside the circular boundary.

A circular water tank is centered at (–5, 2) with a radius of 10 meters. Write the equation in general form.

A school designs a small circular jogging track centered at the origin with a radius of 25 meters. Write the equation of the track.