Frequently Asked Questions...
Work out equation of a curve from eccentricity and a focus?
How do you do it?
For example, if a hyperbola had an eccentricity of 3 and a focus on (0, 1), what would be the equation of the hyperbola?
this may be useful:
http://upload.wikimedia.org/wikipedia/commons/f/fb/Excentricidad.svg
Answer:
Question Too Vague.
A smallish thesis could be made out
as an answer.
Give us actual problems and then, perhaps,
we can give you something you can use.
EDIT : Now, e = 3 and S = ( 0, be ) = ( 0, 1 ).
...........So be = 1......b(3) = 1......b = 1/3....b^2 = 1/9
Hence, a^2 = b^2 ( e^2 - 1 ) = (1/9)( 3^2 - 1 ) = 8/9
so that the hyperbola is
( y^2 / b^2 ) - (x^2/ a^2 ) = 1
[ y^2 / ( 1/9) ] - [ x^2 / ( 8/9 ) ] = 1
9y^2 - ( 9x^2 / 8 ) = 1
72 y^2 - 9 x^2 = 8. ...............Ans.
.........................................................................................
See ? I kept my promise. I came back.
..........................................................................................
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