Answer: [tex]\bold{\dfrac{(x+2)^2}{4}+\dfrac{(x+1)^2}{9}=1}[/tex]
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)
↓ ↑ ↓ ↑
[tex]\dfrac{4}{2}[/tex] = (2)² [tex]\dfrac{2}{2}[/tex] = ( 1 )²
9(x + 2)² + 4(y + 1)² = 36
Divide everything by 36:
[tex]\dfrac{9(x+2)^2}{36}+\dfrac{4(y+1)^2}{36}=\dfrac{36}{36}[/tex]
Simplify:
[tex]\dfrac{(x+2)^2}{4}+\dfrac{(y+1)^2}{9}=1[/tex]
