Question 877320
find a b C and the center and sketch the graph of the ellipse 
4x^2 + 25 y^2 +16 X - 150y + 141=0
4x^2+16 x + 25 y^2  - 150y = -141
complete the square:
4(x^2+4x+4)+25(y^2-6y+9) =-141+16+225
4(x+2)^2+25(y-3)^2=100
{{{(x+2)^2/25+(y-3)^2/4=1}}}
This is an equation of an ellipse with horizontal major axis.
Its standard form of equation:{{{(x-h)^2/a^2+(y-k)^2/b^2=1}}}
For given ellipse:
center:(-2,3)
a^2=25
a=5
b^2=4
b=2
c^2=a^2-b^2=25-4=21
c=√21
see graph below:
y=±(4-(4/25)(x+2)^2)^.5+3

{{{ graph( 300, 300, -10, 10, -10, 10,(4-(4/25)(x+2)^2)^.5+3,-(4-(4/25)(x+2)^2)^.5+3) }}}