Question

The equation of a circle is given below (x+9)^2+(y-46)^2=123

Answer 1

center: (-9,46). Radius: 11.09

Explanation:

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Answer 2

The center of the circle is (-9, 46), radius is 11.09053 and the diameter is 22.18, if the equation of circle is
`(x+9)^(2) +(y-46)^(2)= 123`.

Explanation:

The given is,

`(x+9)^(2) +(y-46)^(2)= 123`

Step:1

Equation of circle is,

`(x-h)^(2) +(y-k)^(2)= r^(2)`...................(1)

Where,

(h, k) - Center of circle

r - Radius of circle

From given,

`(x+9)^(2) +(y-46)^(2)= 123`...............(2)

Comparing equation (1) and equation (2),

Center - (h, k) = (-9, 46)

`r^(2) = 123`

Take square root on both sides,

`r = √(123)`

= 11.09053

r ≅ 11.09053

Formula for diameter,

`d =2r`

Substitute the value of r,

`= (2)(11.09053)`

`=22.18`

diameter, d = 22.18

Result:

The center of the circle is (-9, 46), radius is 11.09053 and the diameter is 22.18, if the equation of circle is
`(x+9)^(2) +(y-46)^(2)= 123`.