so ... what did you determine for the expression in terms of t ?
I'm trying to solve this problem, but I am having trouble. Can someone give me some pointers?
A curve is defined by the parametric equations:
x = 2t / (1 + t^2)
y = (1 - t^2) / (1 + t^2)
By considering the expression x^2 + y^2, eliminate the parameter t to obtain the Cartesian (x-y) equation of the curve.
Thanks
Hello, everyone!
This problem (and solution) involves a paradox.
Paramtric equations: .
Cartesian equation: .
From [3], we have a circle with center at the Origin and radius 1.
. . It has -intercepts and -intercepts
Let's determine the intercepts using the parametric equations.
For -intercepts, let
Substitute into [1]: .
The -intercepts are: .
For -intercepts, let
Substitute into [2]: .
The -intercept is . . . There is only one!
Where is the other -intercept?