Question 439456
We rewrite the equation in the form:{{{25x^2+50x+25+4y^2=75+25}}} simplify:

{{{25(x+1)^2+4y^2=100}}}, divide both sides by 100 and have:

{{{(x+1)^2/4+y^2/25=1}}}, which is the equation of ellipse centered at (-1, 0).

the vertices are:(-1, 5) and (-1, -5).

The foci are: {{{c^2=b^2-a^2}}} => {{{c^2=25-4}}} => c=+/-sqrt(21) and the foci:

(-1, {{{sqrt(21)}}}) and (-1,-{{{sqrt(21)}}}).

{{{drawing(300, 300, -5, 5, -5, 5, grid(1),  ellipse(-1, 0, 2, 5))}}}