How do you write the equation of a circle with its center at (7, 6) and a radius of 2?

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To write the equation of a circle, we use the standard form of the equation, which is given as:

(x – h)2 + (y – k)2 = r2

In this equation:

  • (h, k) represents the coordinates of the center of the circle.
  • r is the radius of the circle.

Given that the center of the circle is (7, 6) and the radius (r) is 2, we can identify:

  • h = 7
  • k = 6
  • r = 2

Now, we substitute these values into the standard form:

(x – 7)2 + (y – 6)2 = 22

Calculating 22 gives us 4, so the equation simplifies to:

(x – 7)2 + (y – 6)2 = 4

This is the equation of the circle centered at (7, 6) with a radius of 2. You can visualize this circle on a coordinate plane where all points (x, y) that satisfy this equation fall on the boundary of the circle. Enjoy exploring the geometric properties of this circle!

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