In Exercises 21-40, 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 oft. (If an interval for t is not specified, assume that
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- Sketch and describe the orientation of the curve given by the parametric equations x=2tandy=4t2+2,2t2.arrow_forwardShow that the graph of the parametric equations x = a + (c − a)t, y = b+(d−b)t, t ∈ [0, 1] is a line segment from (a, b) to (c, d ).arrow_forwardFind the length of the curve r = 2 sin^3 (u/3), 0 … u … 3pi , in the polar coordinate plane.arrow_forward
- Eliminate the parameter t from the parametric equations x = 3 cos t, y = 5 sin t and then sketch the graph of the plane curve.arrow_forwardFind the parametric equation of the line passing through the points P = (1, 2, −1) and Q = (1, −1, −2).arrow_forwardFor the given parametric equations, find the points (x, y) corresponding to the parameter values t = -2, -1, 0, 1, 2. x = t2 + t, y = 3t+1arrow_forward
- What is the rectangular form of the parametric equations? x(t)=t−3,y(t)=2t2−1, where t is on the interval [−2,2]. Enter your answer in the box in standard form.arrow_forwardFind the length of the curve r = 2 sin^3 (u/3), 0<=u<=3pai, in the polar coordinate plane.arrow_forward9.1.2 Sketch the plane curve defined by the given parametric equations, and find an x-y equation for the curve. x=1+2cos(t) y=-2+2sin(t)arrow_forward
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