Question 296335
By "solve" you probably mean "write in standard form" {{{(x^2/a^2)-(y^2/b^2) = 1}}} This is the standard form of an equation of a hyperbola with center at (0, 0) and vertices on the x-axis.
{{{4x^4-9y^2 = 9}}} Divide both sides by 9.
{{{(4/9)x^2-y^2 = 1}}} Notice that {{{4/9 = (2/3)^2}}} and {{{(2/3)^2 = 1/(3/2)^2}}} so you can rewrite the first term:
{{{(x^2/(3/2)^2)-y^2 = 1}}}
Comparing this with:
{{{x^2/a^2 - y^2/b^2 = 1}}} you can see that:
{{{a = (3/2)}}} and {{{b = 1}}}