the points of intersection of the curves whose parametric equations are x=t^2+1 , y=2t and x=2s , y=2/s is given by ?
Hello Varma, by the first set 4 x = 4 t^2 + 4
And y^2 = 4 t^2
So we have 4 x = y^2 + 4 --(1)
By the second set, xy = 4--(2)
Now (1) * y gives
4 x y = y^3 + 4 y
Plug from (2)
16 = y^3 + 4 y
Or y^3 + 4 y - 16 = 0
==> y = 2
So x = 2
(2,2) is the point of intersection
And y^2 = 4 t^2
So we have 4 x = y^2 + 4 --(1)
By the second set, xy = 4--(2)
Now (1) * y gives
4 x y = y^3 + 4 y
Plug from (2)
16 = y^3 + 4 y
Or y^3 + 4 y - 16 = 0
==> y = 2
So x = 2
(2,2) is the point of intersection