Question

Write the equation of the circle with the given center and radius.

#1. Center: (0,2) ; radius: 5

#2. Center: (-4,-5) ; radius: square root ✔️2

#3. Center: (-1,3) ; radius: 8

#4. Center: (9,0) ; radius: ✔️3

Answer 1

Explanation:

The standard equation of a circle is
`(x - h)^2 + (y - k)^2 = r^2`

Center = (h, k)

#1

Center = (0,2)

h = 0

k = 2

r = 5

`(x - h)^2 + (y - k)^2 = r^2`

`(x - 0)^2 + (y - 2)^2 = 5^2`

#2

Center = (-4,-5)

h = -4

k = -5

r =
`√(2)`

`(x - h)^2 + (y - k)^2 = r^2`

`(x - (-4))^2 + (y - (-5))^2 = √(2)^2`

`(x + 4))^2 + (y + 5))^2 = √(2)^2`

#3

Center =(-1,3)

h = -1

k = 3

r = 8

`(x - h)^2 + (y - k)^2 = r^2`

`(x - (-1))^2 + (y - 3)^2 = 8^2`

`(x + 1)^2 + (y - 3)^2 = 8^2`

#4

Center: (9,0)

h = 9

k = 0

r =
`√(3)`

`(x - h)^2 + (y - k)^2 = r^2`

`(x - 9)^2 + (y - 0)^2 = √(3)^2`