Question 795185
Complete The Square for the x and for the y, and then simplify into whichever standard for will be suitable to the type of conic section.


{{{x^2+25y^2+6x-100y+9=0}}}
{{{x^2+6x+25y^2-100y+9=0}}}
{{{(x^2+6x)+ 25(y^2-4y)+9=0}}}
And continuing without explanation for this step section,
{{{(x^2+6x+9)+25(y^2-4y+4)+9=9+25*4}}}
{{{(x+3)^2+25(y-2)^2=100}}}
The squares are now completed.
{{{(1/100)((x+3)^2+25(y-2)^2)=100/100}}}
{{{highlight((x+3)^2/10^2+(y-2)^2/2^2=1)}}}


Compare that to standard form of an ellipse: {{{(x-h)^2/a^2+(y-k)^2/b^2=1}}},
where a is the distance from either vertex to the center along the x axis, b is the distance from either vertical vertex to the center along the y axis; if assuming center were on the origin --- although for YOUR example, center is NOT...
Standard Form for ellipse conventionally uses a for the longer axis and b for the shorter axis.
and the center point is (h,k).


The center point for your example is (-3, 2).