Write the equation in standard form for the circle with center (1, 0) passing through (1, 9/2)

(x - 1)² + y² = 81/4

Explanation:

First, we need to calculate the distance from (1, 0) to (1, 9/2). This distance is equal to

9/2 - 0 = 9/2

Because they both have the same x-coordinate. It means that the radius of the circle is 9/2.

Then, an equation of a circle with radius r and center (h, k) is

(x - h)² + (y - k)² = r²

Replacing (h, k) = (1, 0) and r = 9/2, we get

(x - 1)² + (y - 0)² = (9/2)²

(x - 1)² + y² = 81/4

Therefore, the answer is

(x - 1)² + y² = 81/4