Answer
$(12(-1+\sqrt {5}),0)$
Work Step by Step
$\dfrac{x^2}{a^2}-\dfrac{y^2}{b^2}=1$
$\implies \dfrac{x^2}{a^2}-\dfrac{y^2}{c^2-a^2}=1$
$\implies \dfrac{(24)^2}{a^2}-\dfrac{(24)^2}{576-a^2}=1$
$\implies a^4-1728a^2+331776=0$
$\implies (a^2-24a-576) (a^2+24a-576)=0$
or, $a=12(-1+\sqrt {5})$
The coordinates of the vertex are: $(12(-1+\sqrt {5}),0)$
