Question

Show that the parametric equations x=-e^2t and y=e^t are equal to the Cartesian equation x^2-y^4= 0when -inf 13 years ago

Answer 1

x^2-y^4 =0

?

Answer 2

Yes I forgot to put that in

Answer 3

all right , sub x=-e^2t and y=e^t into the equation

Answer 4

How could you plug them into x^2-y^4 when you are trying show that?

Answer 5

you are showing that (or proving that)
IF x = -e^(2t) and y = e^t THEN x^2 -y^4 = 0

Answer 6

and the latter is a cartesian equation

Answer 7

x=- e^2t

x^2 =-(e^2t)^2= - e^4t

Answer 8

x^2 = e^(4t) ,

Answer 9

Where did the negative sign go when you squared -e^(2t)

Answer 10

when you square a negative it becomes positive

Answer 11

So you can just include the negative as part of the number.

Answer 12

im not sure what youre asking

Answer 13

Claim: IF x = -e^(2t) and y = e^t THEN x^2 -y^4 = 0
Proof:
Suppose x = -e^(2t) and y = e^t

then by substitution
x^2 - y^4 = (-e^(2t))^2 - (e^t)^4 = e^(4t) - e^(4t) = 0

Answer 14

I see what you are saying

Answer 15

but it is not obvious how they got this cartesian equation