An air traffic controller working on the naval aircraft carrier sends out a patrol aircraft to scouts for ships in the area. The patrol aircraft uses radar to detect objects within
a certain radius of itself. This area within the field of the radar is thus a circle with
the patrol aircraft at the center. However, since the patrol aircraft is scouting on
behalf of the aircraft carrier, an xy −coordinate plane is used with the aircraft carrier
at the origin.

The patrol aircraft finds four ships on the outer boundary of its radar field: one is
17.78 km east and 176.78 km north (directly northeast) of the carrier, the second
one is 106.07 km south and 106.07 km west (directly southwest), the third one is
150 km east and 40 km north, while the fourth one is 70 km east and 6 km south of
the carrier.

Find the coordinates of the patrol aircraft the moment it detects the four ships. Write
the equation in standard form for the outer boundary of radar coverage. Determine
whether a ship at 90 km east and 150 km south of the carrier is visible on the radar
of the patrol aircraft. Justify your answer.