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MissPhiladelphia
The standard equation of a circle is

(x-h)^2 + (y-k)^2 = r^2

where the center is at point (h,k)

From the statement of the problem, it is already established that h = 2 and k = -5. What we have to determine is the value of r. This could be calculated by calculating the distance between the center and point (-2,10). The formula would be

r = square root [(x1-x2)^2 + (y1-y2)^2)]
r = square root [(2--2)^2 + (-5-10)^2)]
r = square root (241)
r^2 = 241

Thus, the equation of the circle is

[tex] (x-2)^{2} + (y+5)^{2} =241[/tex]
xero099

The equation of the circle with center C(x,y) = (2, -5) that passes through the point P(x,y) = (-2, 10) is describe by the expression (x - 2)² + (x + 5)² = 241.

How to determine the equation of the circle

By analytical geometry we understand that the equation of the circle is described by the following expression:

(x - h)² + (y - k)² = r²     (1)

Where:

  • r - Radius.
  • h, k - Center of the circle.

The radius of the circle is found by the following Pythagorean expression:

[tex]r = \sqrt{(-2-2)^{2}+[10-(-5)]^{2}}[/tex]

r ≈ 15.524

Hence, the equation of the circle with center C(x,y) = (2, -5) that passes through the point P(x,y) = (-2, 10) is describe by the expression (x - 2)² + (x + 5)² = 241.

To learn more on circles: https://brainly.com/question/11833983

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