Question

A wildlife researcher is monitoring a black bear that has a radio telemetry collar with a transmitting range of 16 miles. The researcher is in a research station with her receiver and tracking the​ bear's movements. If we put the origin of a coordinate system at the research​ station, what is the equation of all possible locations of the bear where the transmitter would be at its maximum​ range?

Answer 1

The equation of all possible locations of the bear where the transmitter would be at its maximum​ range is
`x^2+y^2=256`.

Explanation:

Consider the provided information.

Let the origin of a coordinate system at the research​ station, and the range is 16 miles.

That meas the maximum distance bear can cover is 16 miles and bear can move in any direction.

Center (0, 0) = (h, k)

The equation of circle with center at origin is:

`x^2+y^2=r^2`

Where r is the radius.

Substitute r = 16 in above formula.

`x^2+y^2=(16)^2`

`x^2+y^2=256`

Hence, the equation of all possible locations of the bear where the transmitter would be at its maximum​ range is
`x^2+y^2=256`.