Question

Enter the equation for the circle shown in the graph.

Answer 1

Answer:
`(x\text{ + 1\rparen}^2\text{ + \lparen y - 2\rparen}^2\text{ = 9}`

Step-by-step explanation:

Given:

A circle on a coordinate plane with a dot representing the center

To find:

Equation of the circle

The formula for the equation of a circle is given as:

`\begin{gathered} (x\text{ - h\rparen}^2+\text{ \lparen y - k\rparen}^2\text{ = r}^2 \\ where\text{ center = \lparen h, k\rparen} \\ radius\text{ = r} \end{gathered}`

Identifying the coordinate of the center and the unit for the radius:

Center (h, k) = (-1, 2)

h = -1, k = 2

radius = 3 units from the center to the circumference

r = 3

substitute the values into the formula:

`\begin{gathered} (x\text{ - \lparen-1\rparen\rparen}^2\text{ + \lparen y - 2\rparen}^2=\text{ 3}^2 \\ \\ The\text{ equation:} \\ (x\text{ + 1\rparen}^2\text{ + \lparen y - 2\rparen}^2\text{ = 9} \end{gathered}`