A point P(x, y) moves in a coordinate plane such that the sum of the squares of its distances from both coordinate axes is always equal to 16. What geometric shape is represented by the path (locus) of P?

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A A straight line passing through the origin
B A square with side lengths of 4 units
C A circle centered at the origin with a radius of 4 units
D A parabola opening upwards

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Answer: C. A circle centered at the origin with a radius of 4 units

Answer: C) A circle centred at the origin with a radius of 4 units
Explanation: The distance of P(x, y) from the y-axis is |x| and from the x-axis is |y|.
So x² + y² = 16, which is the equation of a circle with centre (0, 0) and radius 4.

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A point P(x, y) moves in a coordinate plane such that the sum of the squares of its distances from both coordinate axes is always equal to 16. What geometric shape is represented by the path (locus) of P?

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