conjugate hyperbola parameters (1 Viewer)

[barbernator]

I asked this question before, but I was a bit vague in my question and nobody seemed to understand.

As proved, the parametric equations for a regular hyperbola are x= asec(theta), y= btan(theta)

When referring to an ellipse, to have the major axis being along the x axis, or the y axis just depends upon the value of a and b in the ellipses respective parametric equations.

For a hyperbola, changing the values of a and b in the parametric equations just changes the angle between the asymptotes, but does not define whether it is a regular or a conjugate hyperbola. Does anyone know the parametric equations for a conjugate hyperbola?

thanks

 

[Carrotsticks]

Think about it, the parameter coordinates x=asec theta and y = btan theta are appropriate for the hyperbola because the equation of the hyperbola is:



And we use the Pythagorean Identity:



Now, the conjugate hyperbola is defined to be:



What Trig Identity do you think satisfies this...?

 

[barbernator]

Think about it, the parameter coordinates x=asec theta and y = btan theta are appropriate for the hyperbola because the equation of the hyperbola is:



And we use the Pythagorean Identity:



Now, the conjugate hyperbola is defined to be:



What Trig Identity do you think satisfies this...?

ohh gee too easy! thanks carrot