Question

Determine the center and radius of the circle with equation (x+3)² + (y − 2)² = 16​

Answer 1

Answer: Center: (-3, 2). Radius: 4.

Explanation:

The x-coordinate of the center of the circle is given by the constant within the parenthesis with variable x. Whatever number makes the equation x + 3 = 0 is the x-coordinate of the center of the circle, which in this case is -3.

The y-coordinate of the center of the circle is given by the constant within the parenthesis with variable y. Whatever number makes the equation y - 2 = 0 is the y-coordinate of the center of the circle, which in this case is -2.

The radius of the circle is the square root of the constant on the other side of the equation. So, r =
`√(16)` = 4.

The explanation is from the equation of a circle in a graph:

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

h and k in this equation stand for the coordinates of the center of the circle, with h being the x-coordinate and k being the y-coordinate. IN your equation, we have:

`(x+3)^2 + (y-2)^2 =16`

Which can also be written as

`(x-(-3))^2 + (y-(2))^2=16`

See the correlation of numbers -3 and 2 with h and k?

Notice also how the equation contains
`r^2`, so to find the radius you do
`√(r^2)`.