Hyperbolae (1 Viewer)

[sasquatch]

These questions are weird!

Sketch the following and show that they represent rectangular hyperbolas.

and the next one,

Show that the following equationjs represent hyperbolas and find their centre, foci and the equation of their directrices and asymptotes.

How do you show an equation is a hyperbola or rectangular hyperbola?

 

[Trev]

What equations were you given?

 

[sasquatch]

Well for the first question (rect. hyperbolae),

x² - y² = 12
2xy - 3x - y - 2 = 0
etc...

and for the other question (just hyperbolae)

(x -3)²/64 - (y + 1)² = 1
etc..

 

[Templar]

A hyperbola is rectangular if its asymptotes are at right angles to each other.

 

[sasquatch]

How bout the second part.. i thought to show that an equation was a hyperbola, it could be written in the form x²/a² - y²/b² = 1..

but if you see the first question is already in this form :| so im confused...

 

[pLuvia]

You could use the parametric equations to show that it is a hyperbola, and show the general formula

 

[sasquatch]

but the parametric form of (x-3)<sup>2/sup]/64 - (y + 1)2/ 36 = 1

is x = 8sec@ + 3, y = 6tan@ - 1, so by selecting these parametric equations arent you already using the definition of a hyperbola to show its a hyperbola? I was thinking to show it's eccentricity was greater than one.. but that seems to be the same.. using its definition..blah blah..yeah..


EDIT: About rect. hyperbolae, when graphing do you need to indicate the directricies and foci?</sup>

 

[onebytwo]

well it usually depends on the question.
if it is a purely graphical question asking to show features then, of course, you would

 

[jarrypan]

x^2-y^2= a constant
this is a rectangular hyperbola...