Question

How do I eliminate the parameter to find a Cartesian equation of the curve? (See problem below, please)

Answer 1

\(\ \Huge x=t^2, y=6-3t \).

Answer 2

here t=(6-y)/3
so x=((6-y)/5)^2

Answer 3

So basically do you solve for t and then substitute that in to the next equation?

Answer 4

solve t in terms of x, and sub it into the y part

Answer 5

yes

Answer 6

@amistre64 So, in this case t=sqrt(x), so I get \(\ -3\sqrt{x}+6 ?\)

Answer 7

y= that is.

Answer 8

keep in mind the t^2 has 2 solutions; and that the true nature of the curve, if convention is followed, would result in 2 equations for y

but yes

Answer 9

2 Equations?

Answer 10

\[t^2=x\to\ t=\pm\sqrt{x}\]
sub into y= to get:\[y=6\pm3\sqrt{x}\]

Answer 11

That makes sense. Thank you, @amistre64!

Answer 12

youre welcome; matricks is fine to depending on how conventional they want the cartesian equation