Question

X^2+y^2-2x+6y=-3.What are the coordinates of the center and the length of the radius of the circle?

Answer 1

Given:

`x^2+y^2-2x+6y=-3`

is given as the equation of circle.

Required:

The coordinates of the center and the length of the radius of the circle.

Step-by-step explanation:

The general equation of circle is

`x^2+y^2+2gx+2fy+c=o`

where

`\begin{gathered} center=(-g,-f) \\ and \\ radius=\sqrt[]{g^2+f^2-c} \end{gathered}`

now by comparing the general and given equation we get

`\begin{gathered} g=-1 \\ f=3 \\ c=3 \end{gathered}`

now substitute in the formulas

`center=(-g,-f)=(1,-3)`
`radius=\sqrt[]{g^2+f^2-c}=\sqrt[]{7}=2.65`

Final answer:

`\begin{gathered} center=(1,-3) \\ and \\ radius=2.65 \end{gathered}`