Running path locus

Geometry Level 3

Brent is planning his running route. He would like the route to meet the following conditions:

  • He will start at his house, located at \((0,0)\).
  • He will travel in a straight line to some point, \(\text{A}\).
  • He will then travel in a straight line to the school, located at \((8,0)\) (8 km east of his house).
  • Finally, he will travel in a straight line back to his house.
  • He would like the entire route to be exactly 18 km (a distance of 18 units in the coordinate plane).

Which of these is an equation of the locus of points that Brent could select as point \(\text{A}\) in his running route?

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