Question

For the circle with equation (x-2)² + (y+3)² = 9, what are the center coordinates?

Answer 1

`\large\boxed{(2, -3)}`

Explanation:

`\textsf{We are asked for the Center Coordinates given a circle.}`

`\large\underline{\textsf{What is a Circle?}}`

`\textsf{A Circle is a curved shape that is commonly used to present a equidistant (same}`

`\textsf{distance apart) from a Center point.}`

`\textsf{When we create an equation for a circle, we should keep in mind of what the}`

`\textsf{coordinates of the center point are, and the Radius. For this problem an equation}`

`\textsf{has been given to us.}`

`\boxed{\begin{minipage}{20 em} \\ \underline{\textsf{\large Equation of a Circle (Standard Form);}} \\ \\ \tt \tt (x-h)^(2) + (\tt y-k)^(2) = r^(2) \\ \\ \underline{\textsf{\large Where;}} \\ \textsf{h represents the x-coordinate of the center.} \\ \textsf{k represents the y-coordinate of the center.} \\ \tt r^(2) \ \textsf{represents the radius of a circle squared.} \end{minipage}}`

`\textsf{*Note that if we are given the formula, the radius is already squared, unless}`

`\textsf{specified in the directions.}`

`\tt (x-2)^(2) + (y+3)^(2) = 9`

`\textsf{Our main focus should be h and k. Notice how both point values are negative.}`

`\textsf{The Center Point is represented as the opposite given to us in the formula.}`

`\underline{\textsf{Find the Opposite of -2 and 3;}}`

`\tt -2 \rightarrow \boxed{2}`

`3 \rightarrow \boxed{-3}`

`\underline{\textsf{Center Coordinates;}}`

`\large\boxed{(2, -3)}`