Answer
$40$ yards
Work Step by Step
We are given the hyperbola;
$625y^2-400x^2=250000$
Bring the hyperbola to the standard form:
$\dfrac{625y^2}{250000}-\dfrac{400x^2}{250000}=1$
$\dfrac{y^2}{400}-\dfrac{x^2}{625}=1$
Determine $h,k,a,b$:
$h=0$
$k=0$
$a^2=400\Rightarrow a=\sqrt{400}=20$
$b^2=625\Rightarrow b=\sqrt{625}=25$
Determine the vertices:
$(h,k-a)=(0,0-20)=(0,-20)$
$(h,k+a)=(0,0+20)=(0,20)$
Draw the hyperbola.
Determine the shortest distance between the houses:
$2a=2\cdot 20=40$ yards
