Point P is given as \((-8, -8)\). To find the coordinates of points Q and R, which are each 66 units away from point P, we can use the fact that points Q and R will be located on a circle centered at P with a radius of 66 units.
The equation of the circle centered at \((-8, -8)\) with a radius \( r = 66 \) is given by:
\[ (x + 8)^2 + (y + 8)^2 = 66^2 \]
Calculating \(66^2\):
\[ 66^2 = 4356 \]
So the equation becomes:
\[ (x + 8)^2 + (y + 8)^2 = 4356 \]
To find specific points Q and R, we can take two points on the circle. For simplicity, let's consider moving horizontally and vertically from point P, representing two directions.
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Moving directly to the right:
- New coordinates: \[ Q = (-8 + 66, -8) = (58, -8) \]
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Moving directly to the left:
- New coordinates: \[ R = (-8 - 66, -8) = (-74, -8) \]
Thus, two points that are each 66 units away from point P are:
- Point Q: \((58, -8)\)
- Point R: \((-74, -8)\)
Additionally, we could find points in other directions (e.g., upwards, downwards, or diagonally), but these are two straightforward solutions.
Furthermore, using trigonometric principles or parametric equations can give us an infinite number of possible locations for Q and R along the circle, but the question asks for two specific points, which we've identified.
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