Question

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

Answer 1

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

Explanation:

type the answer and the question into Desmos, they’ll be on top of each other

Answer 2

Answer:
`\bold{((x+2)^2)/(4)+((x+1)^2)/(9)=1}`

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)

↓ ↑ ↓ ↑

`(4)/(2)` = (2)²
`(2)/(2)` = ( 1 )²

9(x + 2)² + 4(y + 1)² = 36

Divide everything by 36:

`(9(x+2)^2)/(36)+(4(y+1)^2)/(36)=(36)/(36)`

Simplify:

`((x+2)^2)/(4)+((y+1)^2)/(9)=1`