To create a rotary, the Department of Roads and Highways would like to redesign the intersection of Washington Street and Lincoln Avenue so that the edges of the roads are in the shape of two hyperbolas. The hyperbolas are defined by using the existing roads as the asymptotes. Because of the placement of the fire station and the police station, the maximum horizontal distance of the rotary is 330 feet. A surveyor took measure of Washington Street and Lincoln Avenue. Lincoln Avenue’s path is in the ratio of 3 units west for each 2 units north. Washington Street’s path is in the ratio of 3 units east for each 2 units north.
Find the equations of the two hyperbolas that form the edges of the new roads.
Here is a picture of the diagram.
http://blog.360.yahoo.com/blog-GHCOI0cibK_RvZ7fh3TtMNYrOjs9;_ylt=AsYdJpGc.m12jnDTSkQDVZK.AOJ3
Can anyone help me? I'm so confused. Thank you!
2007-07-04 05:03:50 · 2 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
I have always thought that a rotary = a roundabout= a circle..
If the edges of the roads are conjugate hyperbolas, I'm not sure how that works.
If the max horizontal distance of the rotary is 330 feet, then 2a = 330, so a = 165 feet. Since 3a=2b, b = 247.5 feet
So the equation of the hyperbolas are:
x^2/165^2 - y^2/247.5^2 =1 and
y^2/247.5^2 -x^2/165^2 = 1
2007-07-04 05:34:43 · answer #1 · answered by ironduke8159 7 · 1⤊ 0⤋
was that answer correct ?
2016-07-19 07:34:19 · answer #2 · answered by Anonymous · 0⤊ 0⤋