Final answer:
The equation represents the circle's path, which is calculated by finding the midpoint between two given points and then using that midpoint and one of the points to determine the circle's radius. The equation for the circle's path, based on the midpoint and radius, does not perfectly match any of the given options. The correct answer, when written in general form x² + y² = Ax + By, is: x² + y² = 70x − 90y
Step-by-step explanation:
To find an equation for the drone's path, we should recognize that the path it takes is part of a circle. The center of this circle is the midpoint between the two points described in the question, and the radius is half the distance between these two points. Since Russell is at the origin, and the first point mentioned is (−150, −240) and the second is (220, 150), we calculate the center of the circle (Cx, Cy) and its radius (R).
First, find the midpoint (Cx, Cy):
Cx = (−150 + 220) / 2 = 35
Cy = (−240 + 150) / 2 = −45
Then, calculate the radius (R), which is the distance from the midpoint to one of the points:
R = √[(220 − 35)² + (150 + 45)²]
R = √[(185)² + (195)²]
R = √(34225 + 38025)
R = √72250
Now plug the center coordinates and radius into the standard form of a circle's equation (x − h)² + (y − k)² = R²:
(x − 35)² + (y + 45)² = 72250
Expand this equation:
x² − 70x + 35² + y² + 90y + 45² = 72250
x² − 70x + 1225 + y² + 90y + 2025 = 72250
Combine like terms:
x² + y² − 70x + 90y = 72250 - 1225 - 2025
x² + y² − 70x + 90y = 68000
The correct answer, when written in general form x² + y² = Ax + By, is:
x² + y² = 70x − 90y
However, none of the provided options match this equation exactly.