Question

The illustration represents the positions of two planes on a radar screen at an airport control tower. The control tower is located at the origin. The radii of the circles are in miles.

Due to a problem on the ground, the pilots have been told to continue circling the airport and to maintain the same airspeed. The planes are located at the same altitude. Determine the equation of the circle on which the two planes are flying.

Answer 1

• 0, 0
• 8

Explanation:

You want the equation of the circle shown on the radar screen as having a radius of 8 miles, centered at the origin.

Equation of a circle

The equation of a circle with center (h, k) and radius r is ...

(x -h)² +(y -k)² = r²

Application

Your circle is shown as having a radius of 8 miles. It is centered at the same origin where the control tower is located. That means we have ...

(h, k) = (0, 0)

r = 8

Using these values in the circle equation gives ...

(x -0)² +(y -0)² = 8²