6. Eliminate the parameter to find a Cartesian equation of the curve

Calculus
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Consider the following.

x = et − 6,    y = e2t
Eliminate the parameter to find a Cartesian equation of the curve.
Apr 4th, 2015

Since x = exp(t) - 6, we get y = exp(t)^2 = (x+6)^2.

The Cartesian equation is y = (x+6)^2. Note that the exponent must be always positive, so instead of the whole parabola y = (x+6)^2 we get only half of it ( x > -6).

Apr 4th, 2015

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