Question 41280
{{{ -9x^2+36x+4y^2-24y-36=0 }}}
or {{{ 9x^2-36x-4y^2+24y+36=0 }}}

or {{{ -9(x^2-2*x*2 + 2^2) + 4(y^2 - 2*y*3 + 3^2) - 36 + 9*2^2 - 4*3^2 = 0 }}}
or {{{ -9(x - 2)^2 + 4(y - 3)^2 = 36 }}}
or {{{ 4(y - 3)^2 - 9(x - 2)^2 = 36 }}}
or {{{ (4(y - 3)^2)/36 - (9(x - 2)^2)/36 = 36/36 = 1 }}}
or {{{ (y - 3)^2/9 - (x - 2)^2/4 = 1 }}}
or {{{ (y - 3)^2/3^2 - (x - 2)^2/2^2 = 1 }}}
This is the equation of the hyperbolas with transverse axis x = 2 and conjugate axes y = 3 and y = 0 respectively.

{{{graph( 600, 400, -10, 10, -20, 20, 3 + 3*sqrt(1 + 0.25*(x - 2)^2), 3 - 3*sqrt(1 + 0.25*(x - 2)^2))}}}