Question 435222
To get the standard form of the conic {{{16x^2+25y^2-96x-200y=-144}}}, we make the below transformations:

{{{(4x)^2-2*4*12x+144-144+(5y)^2-2*5*20y+400-400=-144}}}

{{{16(x-3)^2+25(y-4)^2=400}}}, divide both sides by 400,

{{{(x-3)^2/25+(y-4)^2/16=1}}}, the final equation represent an ellipse centered at

(3, 4), with major axis 10 and minor axis 8.