Question

Identify the standard form of the equation 4y^2-338x+32y=-169x^2+443

Answer 1

well it looks like a hyperbola...

collect like terms

\[4y^2 + 32y + 169x^2 -338x = 443\]

Answer 2

I did that but i dont know what to do next

Answer 3

ok... so do this

so complete the square for both x and y

\[4y^2 + 32y + 16 + 169x^2 - 338x + 169 = 443 - 16 - 169\]

which becomes

\[(2y + 4)^2 + (13x - 13)^2 = 258\]

hope it helps