Question

100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!

Answer 1

Here is your answer!

Answer 2

`(x - 5)^2 + (y + 2)^2 = 5`

Explanation:

The equation of a circle with a center at (h, k) and radius r is given by:

`\bold{(x - h)^2 + (y - k)^2 = r^2}`

In this case, the center is at (5, -2) and the point that the circle passes through is (4, 0).

The distance between the center and the point is:

`√((5 - 4)^2 + ((-2) - 0)^2) = √(1 + 4) = √(5)`

Therefore, the equation of the circle is:

`(x - 5)^2 + (y + 2)^2 = √(5)^2`

Simplifying the equation, we get:

`\bold{(x - 5)^2 + (y + 2)^2 = 5}` is a required equation