Question

Q10 Q11.) How far apart are the houses at their closest​ point?

Answer 1

from given pic, closest pt is at x=0
625y^2=1000000
25y=+/-1000
y=+/-40
so houses are 40-(-40)=80yards apart
 

Answer 2

Rearranging the hyperbola equation 625y^2 - 1600x^2 = 1000000

(25y)^2 - (40x)^2 = 1000^2

(25y/1000)^2 - (40x/1000)^2 = 1

(y/40)^2 - (x/25)^2 = 1

By property of hyperbola, the semi-major axis length=40

so at the closest, the houses are 40*2 = 80 yards apart