Question

Identify the standard form of the equation by completing the square

Answer 1

`4 x^(2) -9 y^(2) -8x-36y-68=0`


`4 x^(2) -8x-(9 y^(2) +36y)-68=0`


`(2x)^(2) -2*(2x)*2-((3y)^(2) +2*(3y)*6)-68=0`

add and subtract 2^ to the x-expression and 6^ to the second expression to complete the square.


`[(2x)^(2) -2*(2x)*2+4]-4-((3y)^(2) +2*(3y)*6+36-36)-68=0`


`(2x-2)^(2) -4-((3y+6)^(2) -36)-68=0`


`(2x-2)^(2) -(3y+6)^(2) -4+36-68=0`


`(2x-2)^(2) -(3y+6)^(2) -36=0`


`(2x-2)^(2) -(3y+6)^(2) = 6^(2)`

divide by 6 squared


`( (2x-2 )/(6) )^(2) -( (3y+6)/(6) )^(2) =1`


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


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

Answer: A