Question

A circle in the xy-plane is centered at (3, 0) and has a radius with endpoint (1, 8/3 ). Which answer choice is an equation of the circle?

Answer 1

Answer: (x - 3)² + y² =
`(100)/(9)`

Explanation:

Circle Formula: (x - h)² + (y - k)² = r² ; (h, k) is the center & r is the radius

Use the distance formula for (3, 0) and (1,
`(8)/(3)`)

`r = \sqrt{(x_(2)-x_(1))^(2)+(y_(2)-y_(1))^(2)}`

`r = \sqrt{(3-1)^(2)+(0-(8)/(3))^(2)}`

`r = \sqrt{(2)^(2)+(-(8)/(3))^(2)}`

`r = \sqrt{4+(64)/(9)}`

`r = \sqrt{(36)/(9)+(64)/(9)}`

`r = \sqrt{(100)/(9)}`

`r = (10)/(3)`

****************************************************

Center (h, k) = (3, 0) Radius (r) =
`(10)/(3)`

(x - h)² + (y - k)² = r²

(x - 3)² + (y - 0)² = (
`(10)/(3)`)²

(x - 3)² + y² =
`(100)/(9)`