.
The given equation is an equation of a circle written in general form.
To identify the elements of the circle (its center and the radius) we need to transform the given equation to the standard form.
First step is to divide both sides by 2 to get the leading coefficients at and equal to 1:
=
is your equivalent equation.
Next step is to move the constant term to the right side:
= .
Re-group the terms, collecting x-terms and y-terms in separate groups:
+ = .
Complete the squares separately for x-term and for y-terms
+ = .
Did you noticed that I added the terms to the right side to keep the balance unchangeable ?
Next step is
+ = .
Thus the center of the circle is the point (-2.5,1.5).
The distance from the center to x-axis is 1.5 units.
Solved.
If you want to see more examples/samples of solved problems of this type, look into the lessons
- Standard equation of a circle
- Find the standard equation of a circle
- General equation of a circle
- Transform general equation of a circle to the standard form by completing the squares
- Identify elements of a circle given by its general equation
in this site.
Also, you have this free of charge online textbook in ALGEBRA-II in this site
ALGEBRA-II - YOUR ONLINE TEXTBOOK.
The referred lessons are the part of this online textbook under the topic
"Conic sections: Ellipses. Definition, major elements and properties. Solved problems".