Error in one of your steps:
6 is inside the logarithm as well.
These are normally really easy for me and this one appears to be incredibly simple but I can't seem to get the correct answer.
Given and
Eliminate the parameter to find a Cartesian equation of the curve.
Isolate t:
Plug it into the y equation:
,
Hello, topher0805!
Given: .
Eliminate the parameter to find a Cartesian equation of the curve.
From [1], we have: . x+6)^2" alt="e^t \:=\:x+6\quad\Rightarrow\quad e^{2t} \:=\x+6)^2" />
Substitute into [2]: . x+6)^2" alt="y \:=\x+6)^2" />
This is an up-opening parabola with vertex (-6, 0).
However, note the domains ofCode:|* | | * | *| * | * | --------o------+----- -6 |
The graph is only the "right half" of the parabola.