Question 334885
{{{4x^2- 6y^2 - 8x + 24y - 44 = 0 }}}
{{{4x^2-8x- 6y^2 + 24y - 44 = 0 }}}
{{{4(x^2-2x+1)-6(y^2-4y+4)-44=4-24}}}
{{{4(x-1)^2-6(y-2)^2=4-24+44}}}
{{{4(x-1)^2-6(y-2)^2=24}}}
{{{(x-1)^2/6-(y-2)^2/4=1}}}
Unequal coefficients, unequal signs, this is a hyperbola.
{{{drawing(300,300, -9,9,-6,12 ,graph(300,300, -9,9,-6,12,2+sqrt((4(x-1)^2-24)/6)),graph(300,300, -9,9,-6,12,2-sqrt((4(x-1)^2-24)/6)))}}}