Question

The location of a ship can be found with the use of a hyperbolic model with the path of the ship being described by the hyperbola having two different stations serving as the foci. If the center of the hyperbola is at the origin (i.e., the point (0, 0) on a coordinate plane), and the stations are 212 miles apart, find the equation of the hyperbola if the ship is 90 miles east of the origin.

Answer 1

you really into conics...

Answer 2

and confuse conics :D

Answer 3

I think you should upgrade to quadrics...

Answer 4

ok, determining since the ship is east...so the hyperbola will open left and right
We will have equation is (x-h)^2/ a^2 - (y-k)^2/b^2 =1
Knowing origin or center at (0,0) = (h,k)
Foci is 212 apart therefore, c = 212/2 = 106 mi
Also the ship is 90 miles from the orgin, represent vertex, thefore a = 90 mi
c^2 = a^2 + b^2
106^2 = 90^2 + b^2 => b^2 = 3136
having a and b now
complete the equation

x^2/ 8100 - y^2/3136 = 1

Answer 5

Here is a great summary of hyperbolic curves. http://www.purplemath.com/modules/hyperbola.htm (be sure to click to page 3 for lots of examples!)

Attached is a picture I made in geogebra. :) Hope this helps.

Answer 6

purplemath is great...I just went there to look for the formula for hyperbola :D

Answer 7

It's usual to write the denominators as a square.

Answer 8

you know how to parametrize a circle, right?

So how to parametrize a hyperbola?

Answer 9

lol circle is easier since we only have to deal with the center....but hyperbola is easier to get confuse between a,b and c also when it pens up down or left right....I never like this section :))

Answer 10

Circle is just a special case of ellipse.

For ellipse and hyperbola, focus and directrix the same.

e lessthan 1 or e >1 for hyperbola.

Answer 11

Ellipse - x = a cos t, y = b sin t (now you see the circle,right?)

Hyperbola (a sec t, b tan t) (care with the domain)