Question

Given the following equation for an ellipse: 9x^2+25y^2-18x-50y-191=0

Answer 1

$9x^2+25y^2-18x-50y-191=0\\\therefore 9(x^2-2x+1)+25(y^2-2y+1)-191 -9-25=0\\9(x-1)^2+25(y-1)^2=225\\\therefore \text{Center=(1,1)}\\\text{Let new x and y be X and Y}\\\implies X=x-1 \:;\: Y=y-1\\\implies \frac{X^2}{5^2}+ \frac{Y^2}{3^2}=1$

That's the equation in the standard form, with center as the origin and axes parallel to the coordinate axes.