Answer
$\frac{x^2}{36}-\frac{y^2}{64}=1$
Work Step by Step
Transverse axis is horizontal.
$(±c,0)=(±10,0)$
$c=10$
The equation of the asymptotes when transverse axis is horizontal:
$y=±\frac{a}{b}x$
The equation of the asymptotes:
$y=±\frac{3}{4}x$
So:
$\frac{a}{b}=\frac{3}{4}$
$a=\frac{3}{4}b$
$a^2=\frac{9}{16}b^2$
$c^2=a^2+b^2=\frac{9}{16}b^2+b^2=\frac{25}{16}b^2$
$100=\frac{25}{16}b^2$
$b^2=\frac{1600}{25}=64$
$a^2=\frac{9}{16}·64=36$
Standard form when transverse axis is horizontal:
$\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$
$\frac{x^2}{36}-\frac{y^2}{64}=1$
