Answer
a. $\frac{400x^2}{441}-\frac{400y^2}{3159}=1$
b. See graph.
Work Step by Step
a. Based on the given conditions, we can write the general equation of the hyperbola as
$\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$
with
$2c=6, c=3$
and
$2a=(6sec)(0.35km/sec)=2.1, a=\frac{21}{20}, a^2=\frac{441}{400}$
Thus
$b^2=c^2-a^2=\frac{3159}{400}$
and the equation is
$\frac{400x^2}{441}-\frac{400y^2}{3159}=1$
b. See graph.
