Question 721985
The process needed is Complete the Square, and you do it for the x and for the y.


{{{(4y^2)-(2x^2)-4y+8x-15=0}}}
{{{4y^2-4y-2x^2+8x-15=0}}}
{{{4(y^2-y)-2(x^2-4x)-15=0}}}
The square term to use for y is {{{(1/2)^2=1/4}}} and the square term to use for x is {{{(4/2)^2=4}}}.


{{{4(y^2-y+1/4)-4(1/4)-2(x^2-4x+4)-(-2)(4)=15}}}, combined a step as well as added and subtracted the appropriate square quantities and their results.

{{{4(y-1/2)^2-2(x-2)^2-1+8=15}}}
{{{4(y-1/2)^2-2(x-2)^2=15-7}}}
{{{4(y-1/2)^2-2(x-2)^2=8}}}, now divide each side by 8
{{{highlight((1/2)(y-1/2)^2-(1/4)(x-2)^2=1)}}}


HYPERLOBA.


Note that you might want to see it written as  
{{{highlight(((y-1/2)^2)/2 -((x-2)^2)/4 =1)}}}