Answer:
(x -2)² +(y -3)² = 169
Explanation:
You want the equation of the circle through (7, 15) centered at (2, 3).
Circle equation
The standard-form equation for a circle with center (h, k) and radius r is ...
(x -h)² +(y -k)² = r²
The value of r² can be found using the distance formula.
d = √((x2 -x1)² +(y2 -y2)²)
d² = r² = (7 -2)² +(15 -3)² = 5² +12² = 25 +144
r² = 169
The circle equation is ...
(x -2)² +(y -3)² = 169
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Additional comment
You may recognize the triangle shown in the attachment as having side measures that are the Pythagorean triple {5, 12, 13}. That is, once you see coordinate differences of 5 and 12, you know the circle radius is 13, and r² = 13² = 169.
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