Question 1027261
Okay.
I'm going to start by factoring the -4 away from the "x"s and -104.

{{{ 25y^2-4(x^2+2x+26)=0 }}}

Now, you want to make the X section into a binomial which can be squared easily, and you start by dividing the middle number by 2 and then squaring it to get 1. (sorry if that bit was unclear)

{{{ x^2+2x+1+(25) }}}

Now you have 25 left over. This section of your equation now looks like:

{{{ -4((x+1)^2+25) }}}

Multiply the -4 and 25 to get -100 (which I will move to the other end of the equation). Your entire equation now looks like:

{{{ 25y^2-4(x+1)^2=100 }}}

However, this is not simplified. Now, divide both sides by 100, and you get:

{{{ y^2/4-(x+1)^2/25=1 }}}

If it was just an {{{ x^2 }}}, our center would be at the origin (0,0). However, since it is {{{ (x+1)^2 }}}, we subtract 1 from the center x-coordinate out the 1 in {{{ (x+1)^2 }}}. The y-coordinate was unaffected.

Your center coordinate is (-1,0).