Question

I need this practice problem from my prep guide answered and explained

Answer 1

To rewrite the equation in the indicated form, isolate the variable terms on the left side of the equation.

`8x^2+9y^2-16x-9y=-2`

Group the variable terms and then complete the squares. Add the same terms on the right side of the equation to make it balance.

`\begin{gathered} (8x^2-16x)+(9y^2-9y)=-2 \\ 8(x^2-2x)+9(y^2-y)=-2 \\ 8(x^2-2x+1)+9(y^2-y+(1)/(4))=-2+8+9((1)/(4)) \end{gathered}`

Rewrite the trinomials as squares of binomials and then simplify the right side of the equation.

`8(x-1)^2+9(y-(1)/(2))=(33)/(4)`

To make the right side of the equation equal to 1, multiply both sides of the equation by 4/33.

`\begin{gathered} \mleft((4)/(33)\mright)(8)(x-1)^2+\mleft((4)/(33)\mright)(9)(y-(1)/(2))=\mleft((4)/(33)\mright)\mleft((33)/(4)\mright) \\ (32\mleft(x-1\mright)^2)/(33)+(12(y-(1)/(2)))/(11)=1 \end{gathered}`