Question

Find the center and radius of the circle: (x)² + (y+5)² = 18

Answer 1

The equation of a circle is given by the following formula:

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

Where h and k are the coordinates of the center of the circle and r is the radius. Using this formula find its corresponding values in the equation given:

Use this information to find each of the values of the equation:

`\begin{gathered} (x)^2=(x-h)^2 \\ x=x-h \\ x-x=-h \\ -h=0 \\ h=0 \end{gathered}`
`\begin{gathered} (y+5)^2=(y-k)^2 \\ y+5=y-k \\ k+5=y-y \\ k+5=0 \\ k=-5 \end{gathered}`

The coordinates of the center are (0,-5)

`\begin{gathered} r^2=18 \\ r=\sqrt[]{18} \end{gathered}`

The radius is sqrt 18