QUESTION:
The points of intersection of the curves whose parametric equation are x=t^2+1,y=2t and x=2s and y=2/s is given by:
Options:
a)(1,-3)
b)(2,2)
c)(-2,4)
d)(1,2)
MyApproach:
I have tried to find out the value of t and s by equating the values of x and y. by equating the values of x,i have got a relation 2s^3=1+s^2 and by equating the values of y,i have got t=1/s.I cannot further proceed from here.
Conclusion:
A solution to this problem would be very useful.
Eliminating the parameter in both cases seems to be a good approach. In the first set of equations, if $y = 2t$, then $t = \frac{1}{2}y$. Substituting that into the corresponding $x$ equation gives $x = \frac{1}{4}y^2 + 1$. We do the same thing with the second set of equations, and this gives us $y = 4/x$. Then you can either test the points you're given to find the intersection, or you could plug $y=4/x$ into $x = \frac{1}{4}y^2 + 1$ and solve for $x$.