Find a Cartesian equation for the curve which is defined by the polar equation: r= 6csc(0) where 0<0

Q: ) Write the equation r2+r(sin 0-6 cos 0) = 0 in Cartesian coordinates and identify the corresponding…

A: Solution is given below:

Q: Sketch the curve represented by the parametric equations (indicate the orientation of the curve),…

A: Given the parametric equationsx=2t2y=t4+1

Q: Sketch the curve with the given polar equation by first sketching the graph of r as a function of 0…

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Q: Find a polar equation for the curve represented by the given Cartesian equation. x2 + y2 = 2cx

A: Polar equation for the curve represented by the given cartesian equation x2+y2=2cx is r=2c cosθ The…

Q: The graph of the curve described by the parametric equations x = 2t2 and y =t³ – 3t has a point…

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Q: Find a polar equation for the curve represented by the given Cartesian equation. (Assume 0 ≤ 0 <…

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Q: Find a Cartesian equation from the polar curve 4r sin 0 = 18(rcos 0) +14 1S is

A: Given polar equation is 4rsinθ=18rcosθ2+14  .....1

Q: Find a polar equation of the line with slope -1 that passes through the origin.

A: Given, a line with slope -1 and passes through origin

Q: Find the slope of the line tangent to the polar curve at the given point. 11n r= 4 sin e; - 2,-

A: Given,            r=4sinθ ; -2,11π6

Q: determine the slope of the tangent line to the polar curve r = 1+3 cos(20) at 0 6

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Q: Find the analogous polar equation for horizontal lines in the xy-plane.

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Q: Find a polar equation for the curve represented by the given Cartesian equation. x2+y2=100

A: Here given cartesian equation  x2+y2=102 it is an equation of the circle with radius 10.

Q: Sketch the curve represented by the parametric equations x = t + 1, y = t2 (indicate the orientation…

A: Given: x=t+1, y=t2. first we eliminate t and find equation of curve in x and y x=t+1…

Q: Find the length of the spiraling polar curve r = 3e% From 0 to 27. The length is

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Q: Sketch the curve r = 8+8cos € in polar coordinates.

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Q: 8. x 2t2, y =t + 1 ||

A: We use substitution method to eliminate parameter

Q: Find the equations of the lines tangent and normal to the curve given by the parametric equations…

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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: Graph the curve r2 = 4 cos θ in the Cartesian xy-plane

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Q: Identify the polar curve r = csc 0 by finding a Cartesian equation.

A: The given curve is r=csc θ.

Q: Find a polar equation for the curve represented by the given Cartesian equation. 4y? =

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Q: Find an equation for the tangent line to the polar curve r=θ at  θ=π/2.

A: First find slope and point then use equation of tangent line

Q: Find the length of the spiraling polar curve r = 2e" From 0 to 27. The length is

A: In this question we have to find the length of the spiraling polar curve.

Q: Find an equation (in polar coordinates) of the line tangent to the cycloid x = t - sin t, y = 1 -…

A: Given equations are,

Q: Sketch the curve represented by the parametric equations x = t − 3,                  y = t/(t − 3)…

A: Given: x=t-3                                                  ..1y=tt-3…

Q: Find the points of horizontal and vertical tangency (if any) to the polar curve. r = 3 tan θ

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: Sketch the curve with the given polar equation by first sketching the graph of r as a function of e…

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Q: Find a polar equation for the curve represented by the given Cartesian equation. x2 + y2 = 10cx

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Q: Eliminate the parameter to find a Cartesian equation of the curve with parametric equations x = e^t…

A: Just put the exponential term value from one equation into the other and easily eliminate the…

Q: Consider the curve C of equation 4.xy x² + y? x² + y² From the choices given, select the one that…

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Q: Eliminate the parameter to find a Cartesian equation of the curve. x= cos 21, y=3 sint, 0sts2n

A: To find the Cartesian Equation from the given parametric equations. x = Cos2t  , y = 3Sint , 0 ≤ t ≤…

Q: What is the cartesian coordinates equation of the curve r= 3+ 3secθ given its equation in polar…

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Q: What curve is represented by the given parametric equations, show it on the graph including t, x =…

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Q: Sketch the curve represented by the parametric equations x = t3, y = t2/2 (indicate the orientation…

A: Given a parametric equation,   x=t3                ...(1)  y=t22              ...(2)

Q: Find the polar eauation for the curve represented by the given Cartesian eavation. Dy=-4x² 1.

A: We need to find polar equation.

Q: Find the polar equation of the line y = 3x + 9 in terms of r and ?.

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Q: 3T Plot the points with polar coordinates 3, and (2, 2n) using the pencil. 4

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Q: Give a parametrization of the left half portion of the polar curve described by the equation r = 3.

A: Give a parametrization of the left half portion of the polar curve described by the equation r = 3.

Q: Sketch the curve r = 3 sin 20. a b Show that its Cartesian equation is (x² + y² )° =36x²y²,«

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Q: 2. Find the SA generated by rotating the first quadrant portion of the curve y = 9- x2 about the…

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Q: Sketch the curve given by the parametric equations x= t³ - 1 and y= t² + t.

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Q: Sketch the curve r= cos 2θ

A: Symmetric test for polar coordinates r=f(θ): If f(θ)=f(-θ) then graph is symmetric about polar…

Q: Sketch the curve represented by the parametric equations x = √t, y = t − 5 (indicate the orientation…

A: Given parametric equation, x=t         ...(1)y=t-5       ...(2)

Q: Find the tength of the curve over the given interval Polar Equation Interval

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Q: Eliminate the parameter to find a Cartesian equation of the curve with parametric equations x = et –…

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Q: TRUE OR FALSE. The curve defined by the polar equation r = 2 + 3 sin θ is symmetric with respect to…

A: To determine whether the given statement is true or false.

Q: Find the slope of the tangent line to the polar curve r = 2sinθ +1 at θ= π/4 and then find its…

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