SOLUTION: how far from x-axis is the center of the curve 2x^2+2y^2+10x-6y-55=0

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.