Find the equation of a circle with a center at (7,2) and a point on the circle at (2,5)?

Step-by-step explanation:

We want to find the equation of a circle with a center at (7, 2) and a point on the circle at (2, 5).

First, recall that the equation of a circle is given by:

Where (h, k) is the center and r is the radius.

Since our center is at (7, 2), h = 7 and k = 2. Substitute:

Next, the since a point on the circle is (2, 5), y = 5 when x = 2. Substitute:

Solve for r:

Simplify. Thus:

Finally, add:

We don't need to take the square root of both sides, as we will have the square it again anyways.

Therefore, our equation is:

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