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

A security camera placed at (–8, –4) covers a circular area with radius 9 meters. Write the equation of the coverage area in general form.

A drone takes off from the school courtyard located at the origin. It is programmed not to fly more than 12 meters away. Write the equation representing the maximum flying boundary.

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

The art park is represented by: (𝑥 − 8)2 + (𝑦 + 1)2 = 9. Identify the center and radius. Sketch the circle.

A lake is modeled by: 𝑥2 + 𝑦2 = 81. Sketch the lake.

A Ferris wheel is centered at (3, 6) with radius 15 meters. Write its equation in standard form and convert it to general form.

A radar system is installed at coordinate (0,0). It can detect objects within a radius of 150 km. Write the equation representing the radar detection area.

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.