Question 1090812
4x^2 + 25y^2 -8x+150y + 129 = 0

4(x^2-2x) +25(y^2+6y) + 129 = 0

4((x-1)^2 - 1) +25((y+3)^2 -9) +129 =0

4(x-1)^2 +25(y+3)^2 = -129 + 4 + 225 = 100

(x-1)^2/5^2 + (y+3)^2/2^2 = 1

Ellipse with center on (1,-3) , a=5, b=2 so c=sqrt(25-4)=sqrt(21).

So Focus are F1= (1+sqrt(21),-3) and F2=(1-sqrt(21),-3)

@natolino_