Question

Guys please HELP I really need to understand this ASAP 15 POINTS

thanks!!

Answer 1

The answer to your question is ( x - 2)² + (y + 1)² = 34

Explanation:

Data

(7, -4)

(-3, 2)

Process

1.- Calculate the radius of the circle

Formula

d =
`\sqrt{(x2 - x1)^(2) + (y2 - y1)^(2)}`

Substitution

d =
`\sqrt{(-3 - 7)^(2) + (2 + 4)^(2)}`

Simplification

d =
`\sqrt{(-10)^(2) + (6)^(2)}`

d =
`√(100 + 36)`

d =
`√(136)` =
`2√(34)`

radius =
`√(34) / 2`

radius =
`√(34)`

- Find the center

Xm =
`(7 - 3)/(2) = (4)/(2) = 2`

Ym =
`(-4 + 2)/(2) = (-2)/(2) = -1`

Center ( 2, -1)

Equation of the circle

( x - 2)² + (y + 1)² = 34