Triangle and hyperbola

  • #1
125
5

Homework Statement


Points E and F are the focuses of the hyperbola and point X are on the hyperbola. Determine the size of the main and minor half-axes of the hyperbola.

upload_2019-3-20_11-19-54.png


Homework Equations


x2 = e2 - f2
x = 8

The Attempt at a Solution


I think that eccentricity is 4 units (x/2). But I don’t know how to continue.
 

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Answers and Replies

  • #2
ehild
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How is the hyperbola defined? What is the equation of the hyperbola?
 
  • #3
125
5
A hyperbola is a set of points, such that for any point
b4dc73bf40314945ff376bd363916a738548d40a
of the set, the absolute difference of the distances to two fixed points F1, F2 is constant = 2a

equation....f(x)=1/x
 
  • #4
ehild
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A hyperbola is a set of points, such that for any point
b4dc73bf40314945ff376bd363916a738548d40a
of the set, the absolute difference of the distances to two fixed points F1, F2 is constant =
Correct, What is the name for a?
What is the value of a of the hyperbola shown in the problem?
equation....f(x)=1/x
That is one special hyperbola. Is it the same as the one in the problem?
 
  • #5
125
5
a is semi major axis
use PF2-PF1=2a?
XF-EX=2a......10-6=2a.....a=2cm ?
 
  • #6
ehild
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a is semi major axis
use PF2-PF1=2a?
XF-EX=2a......10-6=2a.....a=2cm ?
Correct!
Where do the semimajor and minor axes appear in the equation of the hyperbola?
Can you draw a hyperbola, with axes parallel with the coordinate axes? What is the equation of such hyperbola?
 
  • #7
125
5
[x^2/a^2] - [y^1/b^2] = 1

a - semimajor axe
b - minor axe
 
Last edited:
  • #8
ehild
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[x^2/a^2] - [y^1/b^2] = 1

a - semimajor axe
b - minor axe
It should be x^2/a^2 - y^2/b^2 = 1
You know a, and the coordinates of the point X : Substitute into the equation of the hyperbola. Calculate b.
 

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