Write an equation of a circle with its center (14, 17) and point on a circle (15, 17).

The equation of a circle is given by the formula (x - h)² + (y - k)² = r², where (h, k) is the center of the circle and r is the radius.

Step 1: Identify the center of the circle (h, k) The center of the circle is given as (14, 17). So, h = 14 and k = 17.

Step 2: Calculate the radius of the circle A point on the circle is given as (15, 17). The radius of the circle is the distance between the center of the circle and any point on the circle. We can calculate this using the distance formula: √[(x2 - x1)² + (y2 - y1)²]. Here, (x1, y1) is the center of the circle and (x2, y2) is a point on the circle. So, r = √[(15 - 14)² + (17 - 17)²] = √[(1)² + (0)²] = √1 = 1.

Step 3: Substitute h, k, and r into the equation of the circle Substituting h = 14, k = 17, and r = 1 into the equation of the circle, we get: (x - 14)² + (y - 17)² = 1² This simplifies to: (x - 14)² + (y - 17)² = 1

So, the equation of the circle with center (14, 17) and a point on the circle (15, 17) is (x - 14)² + (y - 17)² = 1.