What is the equation of a circle with its center at the coordinates (2, 5) and a radius of 12?

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The equation of a circle can be derived from its center coordinates and radius. In general, the standard form of the equation of a circle is given by:

(x - h)2 + (y - k)2 = r2

Here, (h, k) represents the coordinates of the center of the circle, and r represents the radius. Given that the center of the circle is at (2, 5) and the radius is 12, we can substitute these values into the equation:

  • h = 2
  • k = 5
  • r = 12

Now, plugging these values into the standard form:

(x - 2)2 + (y - 5)2 = 122

Calculating the square of the radius:

122 = 144

Therefore, the equation of the circle becomes:

(x - 2)2 + (y - 5)2 = 144

This equation represents all the points (x, y) that are at a distance of 12 units from the center (2, 5).

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