Based on the calculations, the equation for the locus of these points is equal to x² + y² = 9.
How to find the locus of a point?
First of all, we would determine the distance between points A and B as follows:
Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
Distance = √[(-3 - 3)² + (0 - 0)²]
Distance = √[-9² + 0]
Distance = √81
Distance = 9.
Four (4) times the distance between points A and B is given by:
Distance = 9 × 4
Distance = 36.
Translating the word problem into a mathematical expression, we have:
a² + b² = 36
Also, from the distance formula we have:
a = √[(h + 3)² + (k - 0)²]
a² = h² + 6h + 9 + k²
Similarly, b² is given by:
b = √[(h - 3)² + (k - 0)²]
b² = h² - 6h + 9 + k²
Equating the equations, we have:
a² + b² = 36
h² + 6h + 9 + k² + h² - 6h + 9 + k² = 36
2h² + 2k² = 36 - 18
2h² + 2k² = 18
Dividing both sides by 2, we have:
h² + k² = 9 ⇒ x² + y² = 9.
Read more on locus of a point here: https://brainly.com/question/23824483
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