Is (x-h)^4(y-k)=Some Constant Also an Equation of a Rectangular Hyperbola?

[gliteringstar]

the general equation for rectangular hyperbola with vertical and horizontal asymptotes is given as :

(x-h)(y-k)= some constant

Is the following also an equation of rectangular hyperbola

(x-h)^4(y-k)=some constant ?

I am trying to find the shape of this curve,is it similar to that of rectangular hyperbola?

 

[gliteringstar]

...to be more precise...

the cartesian equation of rectangular hyperbola in question is given by:

xy=a^2

If we have it as (x-h)^4(y-k)=a^2,will the shape of graph of this rectangular hyperbola change?...the centre is different of course...it has shifted to (h,k) with the two parts of the graph lying in the newly formed first and third quadrant...

someone please reply!

 

[HallsofIvy]

With the fourth power, it will NOT be a hyperbola at all- though it may look somewhat like one. A "hyperbola", is defined as being one of the "conic sections" and so its equation must be second degree, not fifth degree as you give.

 

[gliteringstar]

thank you :)

But how do we find the graph of such a function?and if not the graph,can we get some idea about point of intersection of graph of this function with any of the axes?