x = 2 cos t, y = 8 sin t; slope = -1

Q: For the parametric equations given below, eliminate the parameter to find the Cartesian equation of…

A: To solve the following parametrized problem

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Q: Given the parametric equations below, eliminate the parameter t to obtain an equation for y as a…

A: Given : x(t) =  e4t, and y(t) = e7t Let x = e4t       e4t = x Taking both side log, log(e4t) =…

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A: Given thatx(t)=t2 and y(t)=lntFrom y(t)=ln(t) we get t=eyThen we plug it in x=t2So, x=ey2or, x=e2y

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Q: Eliminate the parameter and graph the plane curve represented by the parametric equations. Use…

A: Solution: Consider the given equation  x = 4 sin t   ..(1) y = 3 cos t  where 0 ≤ t ≤π      ...(2)…

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Q: Find parametric equations for line that is tangent to the curve x = cos t, y = sin t, z = t at the…

A: given curve is                                   x=costy=sintz=tPoint,cos-4π6, sin-4π6, -4π6t=-4π6

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Q: The slope of the given parametric equation when A= 30 degrees is equal to x = 16 cos A , y= cot A

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Q: The parametric equations x= 8 − 6 sin 3t and y = 8 + 6 cos 3 t for 0 ≤ t ≤ π/4 represent a curve…

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A: Given,x=etandy=e2tNow,we havey=e2ty=et2substituting alue of x above.we get,y=x2This is the equation…

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Q: 73. x = ² – 1, y = t³ + t; t = 2

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Q: How to Graph the following parametric equations by hand, using values of t in [-2,2].make a table of…

A: Given  parametric equation is X = t-2 Y = 2t² So Y = 2*(X+2)² Y = 2X² + 8X + 8

Q: 74. x = sin t, y = cos t; t = T/4

A: Given; x=Sint, y= cost, t=π/4

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Q: Eliminate the parameter t. Then use the rectangular equation to sketch the plane curve represented…

A: We have, the given parametric equation as x=secty=tant As we know that,  sec2t-tan2t=1…

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Q: Ilowing parametric equation x rough the point t = TC Also fi 3

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Q: Eliminate the parameter t. Then use the rectangular equation to sketch the plane curve represented…

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Q: y X 0 A Which ordered pair represents the coordinates of point P? A (-sin 0, -cos 0) B (-cos 0, -sin…

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Q: x = cos 21, y = sin³ 2t; 0 < t < T/4

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Q: Eliminate the parameter t. Then use the rectangular equation to sketch the plane curve represented…

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Q: x = 2 + 5 cos t Consider the parametric equations for 0<t<r. y = 8 sin t (a) Eliminate the parameter…

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Q: A curve has parametric equations given below: x = 2 cot(t), y =2 sin?(t) 0 <t s Find the equation of…

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Q: I= 2 cos(t) lu-3 sin(t) Find the slope of the tangent line to the parametric curve at the point 3…

A: x=2cost,  y=3sint Differentiating with respect to t, we get dxdt=2-sint  &amp;…

Q: The curve given by the following parametric equations; x=sin(8t)+cos(8t),  y=e8t−8t,  0≤t≤π/2 a.)…

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Q: 13. Sketch the Curve by Eliminating the Parameter. a) Sketch the curve and show the direction as t…

A: The objective is to solve the above questions.