Complete the standard form of the equation of the ellipse represented by the equation 9x2 + 4y2 ? 36x + 8y + 4 = 0.

Step-by-step explanation:

Put like terms together:

9x² + 36x + ____ + 4y² + 8y + ____ = -4 + ____ + ____

Complete the square for both terms:

9(x² + 4x +  4   ) + 4(y² + 2y +  1   ) = -4 + 9(4) + 4(1)

          ↓       ↑                   ↓        ↑

          = (2)²                    = ( 1 )²

       9(x + 2)²  +  4(y + 1)²  = 36

Divide everything by 36:

Simplify:

a = 11 : 4

b = 38

c = 1 for every 6