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
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The first set 4 x = 4 t^2 + 4 And y^2 = 4 t^2 So we have 4 x = y^2 + 4 --eq(1) By the second set, xy = 4--eq(2) Now eq (1) * y gives 4 x y = y^3 + 4 y Plug from eq (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
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Find s as x/2 Put in y=2/s so y=x So it satisfies above t^2+1=2t
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