Question 173591
{{{4x^2-24x-9y^2=0}}} lets factor the x terms and complete the square
:
{{{4(x^2-6x+9)-9y^2-9=0}}}
:
{{{4(x-3)^2-9y^2=9}}}now divide all terms by 9
:
{{{(4(x-3)^2/9)-y^2=1}}}
:
{{{(x-3)^2/(3/2)^2-y^2/(1)^2=1}}}
:
this is an equation of an hyperbola

with center at (3,0) 


{{{drawing( 300, 300, -5, 5, -5, 5, 
         grid(1),
         blue( hyperbola( 3,0, 3, 1 ) 
         ))}}}