Question 627828
Standard form for:
2x^2-4y^2+8x-24y-40=0
complete the square
2x^2+8x-4y^2-24y-40=0
2(x^2+4x+4)-4(y^2+6y+9)=40+8-36
2(x+2)^2-4(y+3)^2=12
{{{(x+2)^2/6-(y+3)^2/3=1}}}
This is an equation of a hyperbola with horizontal  transverse axis.
It standard form: {{{(x-h)^2/a^2-(y-k)^2/b^2=1}}}  (h,k)=(x,y) coordinates of center
center: (-2,-3)