Question 979651
Ellipse is the locus point which moves so that the sum of its distances from two fixed points is constant and is equal to the length of the major axis (2a)

1.  General Eqn:  Ax^2 + Cy^2 + Dx + Ey + F = 0

2.  Standard Eqn 
    
    Center at origin C(0,0)
    [(x^2/a^2) + (y^2/b^2)] =1 major axis - horizontal
    [(x^2/b^2) + (y^2/a^2)] =1 major axis - vertical

Center at (h,k) C(h,k)
    [(x-h)^2/a^2) + ((y-k)^2/b^2)] =1 major axis - horizontal
    [(x-h)^2/b^2) + ((y-k)^2/a^2)] =1 major axis - vertical
  
    note: a > b

now substituting values 

  ((x + 2)^2)/4) + ((y-5)^2)/5))=1  - eqn of the ellipse