Question

Identify the radius and center?

1. Identify the radius and the center. `(x-1)^2+(y+3)^2=4`
   Radius = ___Center ( , )

2. Identify the radius and the center. `x^2+(y-3)^2=14`
   Radius = ___ Center ( , )

3. Identify the radius and the center. `y^2+4x-20-2y=-x^2`
   Radius = ___Center ( , )

Answer 1

1. Radius is `sqrt4=2`
   Centre (1,-3)

2. Radius is `sqrt14`
   Centre (0,3)

3. `x^2+4x+y^2-2y=20`
   `(x +2)^2-4+(y-1)^2-1=20`
   `(x +2)^2+(y-1)^2=25`

Radius `sqrt25=5`
Centre (-2,1)

Answer 2

See answers below

Explanation:

Given: `(x-1)^2 + (y+3)^2 = 4; " "x^2 + (y-3)^2 = 14`

`" " y^2 + 4x-20 - 2y = -x^2`

The standard circle equation: `(x-h)^2 + (y-k)^2 = r^2`,

where center = `(h, k)` and the radius `= r`

The first 2 centers come directly from the equation:

1) center `(1, -3), " "r = sqrt(4) = 2`

2) center `(0, 3), " "r = sqrt(14)`

The third equation must be put into standard form by completing the square. Put `x-`terms together and `y-` terms together:

`(x^2 + 4x) + (y^2 - 2y) = 20`

Cut each `x` and `y` constant in half to compete the square and add the addition sum (31/2 constant)^2# to the other side:

`(x +2)^2 + (y-1)^2 = 20 + (2)^2 + (-1)^2`

`(x +2)^2 + (y-1)^2 =25`

3) center `(-2, -1), " "r = sqrt(25) = 5`