Question

Name he center and radius of the following circle (X+2)^2+(y-5)^2=64

Answer 1

Given:

`(x\text{ + 2\rparen}^2\text{ + \lparen y -5\rparen}^2\text{ = 64}`

The standard form of the equation of a circle is:

`\begin{gathered} (x\text{ - h\rparen}^2\text{ + \lparen y - k\rparen}^2\text{ = r}^2 \\ Where\text{ \lparen h, k\rparen are the coordinates of the center } \\ and\text{ r is the radius} \end{gathered}`

Re-arranging the given equation to the form of the standard equation:

`(x\text{ - \lparen-2\rparen\rparen}^2\text{ + \lparen y -5\rparen}^2\text{ = 8}^2`

Hence, the center is (-2, 5) and the radius is 8