Question
In the following exercise eliminate the parameter t. Then use the rectangular equation to sketch the plane curve represented by the given parametric equations.
In the following exercise eliminate the parameter t. Then use the rectangular equation to sketch the plane curve represented by the given parametric equations. Use arrows to show the orientation of the curve corresponding to increasing values of t.
x = 3t + 6, y = 9t^2; -infinity < t < infinity
The rectangular equation is ______ with _____
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Koala Tutor
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The rectangular equation is x = 3t + 6 and y = 9t^2.
To eliminate the parameter t, we can solve the first equation for t and substitute it into the second equation. From the first equation, we have t = (x - 6)/3. Substituting this into the second equation, we get y = 9((x - 6)/3)^2.
Simplifying, we have y = (x - 6)^2
Therefore, the rectangular equation is y = (x-6)^2 with no restrictions on x and y.
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