Question 1065505
A hyperbola that has x-intercepts has an equation of the form
{{{x^2/a^2-y/b^2=1}}} , and its asymptotes are
{{{y=(b/a)*x}}} and {{{y=-(b/a)*x}}} ,
so for this problem
{{{b/a=2}}} <---> {{{b=2a}}} .
That makes the equation
{{{x^2/a^2-y^2/4a^2=1}}} so far.
To find the value for {{{a^2}}} ,
we substitute {{{system(x=9,y=16)}}} ,
the coordinates of point (9,16) .
{{{9^2/a^2}}} {{{"-"}}}{{{16^2/4a^2=1}}}
{{{81/a^2}}} {{{"-"}}}{{{256/4a^2=1}}}
Multiplying both sides of the equal sign times {{{4a^2}}} ,
we get {{{4*81-256=4a^2}}}
{{{324-256=4a^2}}}
{{{68=4a^2}}}
{{{a^2=68/4=17}}}
So, the equation we were looking for is
{{{highlight(x^2/17-y^2/68=1)}}} .