Identify the curve by finding a Cartesian equation for the curve. r2 cos 20 = 1

Q: For each of the described curves, decide if the curve would be more easily given by a polar equation…

A: (a) Given: A line through the origin that makes an angle of,   with the positive x-axis.

Q: find parametric equations for the given curve. y = 9 − 4x

A: The given equation

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A: Given the parametric equations x = 1+1t, y = t -1 x = 1+1t ,      y +1 = t x = 1+1y+1xy+1 = y+2xy…

Q: Find a Cartesian equation for the curve. r2 cos(2?)

A: We have  to find cartesian equation

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Q: Plot the curve r = 1+sin 8. Then find the length of the curve.

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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) =…

Q: ind the Cartesian equation of the curve C traced out by a point whose coordinates, in terms of a…

A: given curve c is traced by point   a cosθ  , b sinθ now Consider     x= a cosθ     ,    y = bsinθ⇒…

Q: For the parametric equations: x(t) = t^2 and y(t) = ln t (a) find a Cartesian equation  (b)…

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

Q: If a = 5 and b = 4, find parametric equations for the curve that consists of all possible positions…

A: Consider the larger right-triangle OAB.

Q: The polar equation for the curve whose rectangular(cartesian)equation xy 2 is: (a)rcos@sine = 4 8…

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Q: a) Eliminate the parameter to find a Cartesian equation of the curve. (b) Sketch the curve and…

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Q: Compare the equation r=2 with its equation in rectangler coordinates. In which coordinate system is…

A: The given equation is r=2.   Square both sides of the equation. r2=22=4   Substitute 4 for r2 in the…

Q: Consider the following. x = et y = e-2t (a) Eliminate the parameter to find a Cartesian equation of…

A: Given, x=ety=e-2t We can write, y=et-2 but x=et ⇒y=x-2⇒y=1x2

Q: Find the parametric equations for, the tangent line to the curve It)=4?+1) i t (t+ 4)Ĵ ť 3+3 R at…

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Q: x = 2 cos(?),    y = 3 sin(?),    −pi/2 ≤ ? ≤ pi/2 Eliminate the parameter to find a Cartesian…

A: Given that x=2 cost and y=3 sin t where -π2≤t≤π2. To eliminate the parameter ,divide first…

Q: Find a Cartesian equation for the curve and identify it. r = 9 cos(8) circle O parabola O limaçon O…

A: here we have,  the polar equation of the curve is ,  r=9cos(θ) ................(1)

Q: Select the curve generated by the parametric equations. Indicate with an arrow the direction in…

A: The given parametric equation is: x=3+t and y=t2-5t, 0≤t≤6 Find the value of t, where y=0:…

Q: find parametric equations for the given curve.  x 2 + y 2 = 49

A: Given: find parametric equations for the given curve.   x2 + y2 = 49=72The parametric equation for a…

Q: Q2/ Identify the symmetry of the curve r= sin e + cos e. Then sketch the curve in xy-plane.

A: Given: r=sin θ+cos θ The symmetry tests for polar graphs. 1. Symmetry about the x-axis: If the point…

Q: T: R² R² rotates points (about the origin) through 31/2 radians (in the counterclockwise direction).

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Q: X =Sint y=DCOs 2t, %3D ミte

A: x= sint , y= cos2t  -π2<x<π2 To find: the Cartesian equation and sketch the curve and indicate…

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: △DFE is rotated 180o about the origin to give △ D’F’E’ Explain how to find these coordinates.

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Q: a) Eliminate the parameter to find a (simplified) Cartesian equation for this curve. (b) Sketch the…

A: We have to find a Cartesian equation for this curve and sketch the parametric curve.

Q: 5. Trace the curve r = sinecos³e.

A: To find the trace of the given curve r=12sinθcos3θ

Q: Find a Cartesian equation for the curve and identify it. 12 cos(20) = 1 o ellipse o limaçon circle o…

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Q: Eliminate the parameter to find a Cartesian equation of the curve. (b) Sketch the curve and indicate…

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Q: 8- For the curve whose Cartesian equation is: (x2 + y?)3/2 = 2x? a. Find and simplify the equation…

A: The given equation is x2+y232=2x2

Q: (a) In the figure below, two secants are drawn to a circle from exterior point E. Suppose that EX=…

A: I have given an answer in step 2.

Q: Find a Cartesian equation for the curve.

A: By using convertion formula for converting polar coordinates in to Cartesian coordinates. We can…

Q: Which graph shows the curve described by the parametric equations? Sx (t) = 2 sin t y (t) = 4 cos t

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Q: Name the type of basic curve that the following pair of equations represents: x = 2 cos(3t), y =…

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Q: Find a Cartesian equation for the curve and identify it. 2 cos(20) = 1 O limaçon O circle O parabola…

A: Given curve  r²cos(2theta) = 1

Q: Sketch the curve represented by the parametric equations x = 2 + 3 cos θ andy = 2 sin θ. Eliminate…

A: The curve represented by the parametric equations x=2+3cosθ and y=2sinθ is shown below,

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Q: 6. Trace the curve r? = 4cos*etan?e. %3D

A: The equation r2=4 cos4 θ tan2 θ can be resolved to get two equations:  r=±2 (cos2 θ)(tan θ)=±2(cos…

Q: Find an equation in Cartestian coordinates for the curve represented below in in polar form. Your…

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Q: a) Eliminate the parameter to find a Cartesian equation of the curve. b) Sketch the curve and…

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Q: Convert the following equation to Cartesian coordinates. Describe the resulting curve. r cos 0 = - 3…

A: here is the solution

Q: in polar coordinates find its length. The curve given by the equation r = -8sin0 a) В) 24п С) 4п O…

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Q: Identify and graph the following curves. a) r2 = cos(2θ) b) r2 = √3 + 2 sin θ c) r = 3 −…

A: Hello. Since your question has multiple sub-parts, we will solve first three sub-parts for you. If…

Q: Find the intercepts and the symmetry for the polar equation r = 1+ sine.

A: Note: since you have posted multiple questions. As per our guidelines we are supposed to solve only…

Q: 6. The Cartesian equation of the curve r=- is 1-cos(0) (Write your answer in the follo

A: Given:   r = 6/( 1 - cos θ)

Q: Consider the following.  x=sin(t), y=csc(t), 0<t<pi/2 Eliminate the parameter to find a Cartesian…

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Q: 9. The Cartesian equation of the curve r=- is 1-cos(0) (Write your answer in the following form y?=…

A: For polar form,  Substitute  r=x2+y2;cosθ=xrsinθ=yr

Q: Find a Cartesian equation for the curve. r = 7 sec(?)

A: Given query is to find the Cartesian equation if the curve.

Q: Trace the curve r = -sinecos e

A: Given: The curve is: r=12 sinθ cos3θ We have to trace the given curve.