Final answer:
The equation of the circle with center (5,-3) and passing through (2, 5) is (x - 5)^2 + (y + 3)² = 34. Equation of circle: (x - 5)² + (y + 3)² = 73, center (5,-3), passing through (2,5).
Step-by-step explanation:
The equation of the circle with center (5,-3) and passing through (2, 5) can be found using the formula:
(x - h)² + (y - k)² = r²
where (h, k) is the center of the circle and r is the radius. Substituting the given values, we get:
(x - 5)² + (y + 3)² = 34
The equation of a circle is given by the formula (x - h)² + (y - k)² = r², where (h, k) is the center and r is the radius. In this case, the center is (5, -3), and it passes through the point (2, 5). To find the radius, we use the distance formula between the center and the given point:
r = √((x2 - x1)² + (y2 - y1)²) = √((2 - 5)² + (5 - (-3))²) = √9 + 64 = √73
Substitute the values into the circle equation:
(x - 5)² + (y + 3)² = (√73)²
(x - 5)² + (y + 3)² = 73
Therefore, the equation of the circle is (x - 5)² + (y + 3)² = 73.