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.

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:

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