Question

1. Eliminate the parameter to find the Cartesian equation for the curve:

y = e^(2t) + 1 and x = e ^t .

Answer 1

so how do we combine parameter equations into a single equation?

Answer 2

would it be y = x^(2) + 1 bc (e^t)^2 = e^2t

Answer 3

and x = e^t

Answer 4

???

Answer 5

dunno, depends on if y is a function of x :)

Answer 6

y is a function of "t"; so I would assume its independant of "x"

Answer 7

Wikipedia: "Converting a set of parametric equations to a single equation involves eliminating the variable t from the simultaneous equations . If one of these equations can be solved for t, the expression obtained can be substituted into the other equation to obtain an equation involving x and y only. If x(t) and y(t) are rational functions then the techniques of the theory of equations such as resultants can be used to eliminate t. In some cases there is no single equation in closed form that is equivalent to the parametric equations."

Answer 8

solve for "t" and substitute it into the other equation.... is what I think it says :)

Answer 9

x = e^t

ln(x) = t

y = e^(2ln(x)) +1

is what I make of it

Answer 10

ok thanks

Answer 11

that can be simplified probably :)

y = e^(2ln(x)) +1

y = e^(ln(x^2)) +1

y = x^2+1

does that make sense?