Answer
$\frac{x^2}{4}+\frac{y^2}{1.75}=1$
or
$\frac{x^2}{4}+\frac{7y^2}{4}=1$
Work Step by Step
Major axis is horizontal.
Foci: $(±c,0)=(±1.5,0)$
$c=1.5$
$e=\frac{c}{a}$
$0.75=\frac{1.5}{a}$
$0.75a=1.5$
$a=\frac{1.5}{0.75}=2$
$a^2=b^2+c^2$
$b^2=a^2-c^2=2^2-1.5^2=4-2.25=1.75$
$b=\sqrt {1.75}$
Equation of the ellipse:
$\frac{x^2}{a^2}+\frac{y^2}{a^2}=1$
$\frac{x^2}{2^2}+\frac{y^2}{(\sqrt {1.75})^2}=1$
$\frac{x^2}{4}+\frac{y^2}{1.75}=1$
$\frac{x^2}{4}+\frac{7y^2}{4}=1$
