Question

Drag each tile to the correct box. Arrange the steps to rewrite the hyperbolic equation 4y^2 − 9x^2 + 54x − 8y − 113 = 0 in standard form. Tiles: Complete the square by adding appropriate numbers on each side of the equation. Change the equation to the standard form by dividing the equation by 36. Group the x terms and the y terms. Continue simplifying to get the equation in standard form. Continue simplifying by writing the trinomials as squares and eliminating constant terms from the left side. Take the common factors outside the brackets and eliminate the constant terms from the left side of the equation. Options: Option 1: Complete the square by adding appropriate numbers on each side of the equation. Option 2: Change the equation to the standard form by dividing the equation by 36. Option 3: Group the x terms and the y terms. Option 4: Continue simplifying to get the equation in standard form. Option 5: Continue simplifying by writing the trinomials as squares and eliminating constant terms from the left side. Option 6: Take the common factors outside the brackets and eliminate the constant terms from the left side of the equation.

Answer 1

Hi,

Explanation:

Many words for nothing.

`4y^2-9x^2+54x-8y-113=0\\\\\Longleftrightarrow\ 4(y^2-2y+1) -4 -9(x^2-6x+9)+81=113\\\\\Longleftrightarrow\ 4(y-1)^2-9(x-3)^2=36\\\\\Longleftrightarrow\ \boxed{((y-1)^2)/(9) -((x-3)^2)/(4) =1}\\`