Answer to Question #255565 in Analytic Geometry for Joshua

Question

1. A duly-licensed engineer designs two houses that are shaped and positioned like a part of the branches of the hyperbola whose equation is 625𝑦2 − 400𝑥2 = 250,000, where x and y are in yards. How far apart are the houses at

their closest point?

Answer 1

$$625𝑦^2 − 400𝑥^2 = 250000$$

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

Vertices: $(0, -20), (0, 20).$

The distance between the closest points is

$$20-(-20)=40(yards)$$

The houses at their closest point are 40 yards apart.