- #1
Frankenstein19
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Homework Statement
Consider the parametric curve
x=ln(t) and
y= 1+t^2
i need to eliminate the parameter to find the cartesian equation
Homework Equations
The Attempt at a Solution
if i solve for t using x I get that t=e^x
but if i solve for t using y i get t=(y-1)^(1/2)
when i plug in x into y i get that y=1+e^2x
but plugging y into x i get that x= ln(y-1)^(1/2)
both of which have different domains of parameterization and i need to find the domain of parameterization
how can i know which to use? which is the correct one?
then part b says that: "since dx/dt=______ it is _____ along the domain of parameterization, the curve goes through ________________" I HAVE NO IDEA WHAT TO PUT THERE
because i thought i had to just put like dx/dt= 1/t and then i thought i had to put concave up or down but if i use y=1+e^x^2's domain i can't do that
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