Question

An architect designs two houses that are shaped and positioned like a part of the branches of the hyperbola whose equation is where and are in yards. How far apart are the houses at their closest point?

Answer 1

Answer:

40 yards

Step-by-step explanation:

Data:

The hyperbola equation is expressed as follows:

$625y^{2} -400x^{2} = 250 000$

Dividing each term by 250 000 gives:

$\frac{625y^{2} }{250 000} - \frac{400x^{2} }{250 000} = \frac{250 000}{250 000}$

$\frac{y^{2} }{400} - \frac{x^{2} }{625} = 1$

thus:

a² = 40

Therefore, the houses will be 20 yards apart.