6 (1). Consider the curve C of equation (x²-2y+y²)² = x²+y². Among the options listed, select the one that correctly shows a possible equation for C in polar coordinates and the equation of a line tangent to the pole. 27 A) C:r=1+2sin(8), With tangent to the pole 3 7T B) C :r=1+2sin(8), With tangent to the pole C) C:r=1-2 cos(6), With tangent to the pole %3D 3 27 D) C:r=1+2 cos(8), With tangent to the pole 3 ||

Q: The curves C1 and C2 are both symmetric with respect to the polar axis. Each of these curves is…

A: As per the question we are given two polar curves C1 , C2 which are symmetric about the polar axis.…

Q: 4) 4+ 3+ -5 -4 -3 -2 3 4 5 r -2+ -3+ -4+ 2.

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Q: 3n Q10:- Show that the point (2,) lies on the curve r=2sin 20. 4

A: 10) Given curve is r=2sin2θ show that (2,3π4) is a point lies on the curve

Q: 3. Draw the polar curve r = 3 +sin 30

A: Solution: The objective is to graph the polar curve r=3+sin(3θ)

Q: A curve with polar equation r = 42 6 sin(0) + 31 cos(0) y = has Cartesian equation:

A: cartesian equation is y=7−631x​Explanation:Step 1:given that r=6sinθ+31cosθ42​using cross…

Q: ). vert the following equation to polar coordinates. Your answer should be expressed in the format r…

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Q: Show that the curve r= sin(0) tan() (called a cissoid of Diocles) has the line x = 1 as a vertical…

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Q: Consider the polar curves C₁ : r = 2 - cas 0 and C₂: r = 2 + 2 cos 0, 0 € [0, 2πC). (1.) Show that…

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Q: Find the Cartesian equation for the curve represented by the polar equation, r = 2 sin 0. O x² + y²…

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Q: 3. Find two different sets of polar coordinates (r. 8) for the point with Cartesian coordinates (x,…

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Q: 3. Rewrite the polar equation in rectangular, rewrite it either as a conic section or in the form y…

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Q: 3. Find a polar coordinates for the point that is described in Cartesian coordinates as (x,y) = (2,…

A: We can solve the given problem using the concept of polar coordinate of given problem.

Q: 13) Sketch the graph of the polar equation r = 2. Label two points. %23

A: It's equation of circle. So I'm providing hand written solution for better understanding.

Q: b) The length in first quadrant of the curve x/3 + y2/3 = a²/3 is given by 6ac/2 where parametric…

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Q: Suppose the parametric equations for a moving charged particle in an electromagnetic field take the…

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Q: Consider the polar curve given by the equation r(0) = 1 - sin(30). It is an example of what is…

A: Graph:

Q: 2 - y = 2 #8) A) Change equation x 4 to polar coordinates.

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Q: Given polar curve r = −6 sin(θ) do the following. (a) Find the Cartesian equation for this curve.…

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Q: 60 50 60 50 40 40 30 30 20 10 20 50 100 150 10 20 40 60 80 (d) Use a graphing utility to approximate…

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Q: Sketch the curve (x2 + y2 )3 =4x2y2 by converting to polar coordinate system

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Q: 5. (i) Find the polar coordinate of the point P(x, y) = (1, v3).Plot the graph (ii) Find the…

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Q: Plot the following curves in polar coordinates. 50 (52) 1. r = 2 + cos

A: We have to graph the given polar curve.   According to our guidelines we can solve only one question…

Q: Consider the polar curve with equation r=1+2cos(θ):   (I) The slope of the tangent line to the curve…

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Q: 1. Transform the polar equation 4 cos 0 cos² 0 + 1 into its Cartesian form and identify the curve.

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Q: 2) Sketch the graph of the curve with the polar equation: r=2- sin(20).

A: The given polar equation is r=2-sin2θ. Draw the graph of the given polar equation in detail.

Q: Find a Cartesian equation for the curve given by the polar equation T = 4 sin 0. 73°F 1. (x - 2)² +…

A: We have to find out