Answer: The standard form of the ellipse is (x+1)^2/25 + (y-4)^2/16 = 1
Explanation:
Separate the terms firstly:
x terms:
16x^2 +32x
By factorisation:
16(x^2 + 2x)
Completing the square by adding (2/2)^2 = 1 inside:
16(x^2 +2x +1) - 16
Simplification:
16(x + 1)^2 - 16 -------------(1)
Now, go with y terms:
25y^2 - 200y
By factorization:
25(y^2 - 8y)
Completing the square by adding (8/2)^2 = 16 inside:
25(y^2 - 8y +16) - 400
Simplification:
25(y-4)^2 - 400 -----------------(2)
Putting (1) and (2) together:
16(x+1)^2 - 16 + 25(y - 4)^2 - 400 +16 = 0
Combine like terms:
16(x + 1)^2 + 25(y - 4)^2 - 400 =0
Divide both sides by -400 :
(x + 1)^2/25 + (y - 4)^2/16 = 1
Therefore, the standard form of the ellipse is (x+1)^2/25 + (y-4)^2/16 = 1