PLs urgent How to find the parametric forms of rectanguler hyperbola and other curves from equations of general curves like of rectangular hyperbola xy = c2 its parametric form is (ct,c/t) How can we get this (ct , c/t) and for other curves too?
Dear student
To find any point (x,y) in 2D space, we have two unknown variables x and y
so we need two equations to solve
in case of rectangular curve xy=c2we can take any point as (ct,c/t).
there is only one known t, as c is already known. This t can be found out by using the other information like the tangent or normal etc at point (ct,c/t) and then get the value for t.
similarly point on any parabola y2=4ax is (at2,2at)
in case of rectangular curve (x+a)(y+b)=c2 we can take any point as (ct-a,c/t-b).
Regards
To find any point (x,y) in 2D space, we have two unknown variables x and y
so we need two equations to solve
in case of rectangular curve xy=c2we can take any point as (ct,c/t).
there is only one known t, as c is already known. This t can be found out by using the other information like the tangent or normal etc at point (ct,c/t) and then get the value for t.
similarly point on any parabola y2=4ax is (at2,2at)
in case of rectangular curve (x+a)(y+b)=c2 we can take any point as (ct-a,c/t-b).
Regards