Write the given polar equation in cartesian form (in terms of x r – 1= cos 0 = Cos 2- y? – 1 = x² +y? V V x² + y? – 1 = 22+y² Vx² + y² – 1 = .2 22 +y² V Va2 + y? + y = r.2.

Q: Use the identity cos 20 = cos² 0 – sin² 0 to find a polar equation of the hyperbola x² – y² = 1.

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Q: Fill in the table below. dt stuumo (e Rectangular Form Polar Form (7) ーπ 5, T,一 7 -7/3 2 2 (0,-3)…

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Q: Let C, D and E be the polar curies below: Cir=f(0) = 3-3 cos 0 E¹r = g(0) = 1/250c4 SOC 3 D:r=3 (1.)…

A: As per the question we are given two curves in polar coordinates as : C : r = f(θ) = 3 - 3cos(θ) E :…

Q: Match the graph with its polar equation. r = 2 sin(0) 1/2 A/2 4 -2 -2 A/2 3- A/2 -1 1 2 4 -2 -1 1 2…

A: Topic :- Geometry Corect Answer= 3 r=2sinθr    θ0    01    π62     π20       π

Q: A Moving to another question will save this response. Question 13 Replace the polar equation with an…

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Q: Solve the following Laplace equation in polar coordinates (r, 0). 1 u + r2 302 u 1 ди =0, for 0<r<…

A: This question is about application of laplace domain analysis

Q: 45. The rectangular equation x² + y² - 2x=0 written in polar form is r = 2 cos.

A: The rectangular equation is x2+y2-2x=0

Q: Graph the family of polar equations r = 1 + c sin 2u for c = 0.3, 0.6, 1, 1.5, and 2. How does the…

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Q: 1. For the polar coordinate (r,0) = (-2,7x/6), give one coordinate rUand -2nsOs 2n.

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Q: Solve the problem. Te 1) Plot the point 2, and find other polar coordinates (r, 0) of the point for…

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Q: The polar equation 9 cos 0 +2 sin0 = in Cartesian form is defined by I Y A. C. 9x +2y=1 +/-/22 - 1 9…

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Q: Convert the given Cartesian equation into a polar equation. x² + y? = 2x + 3y Select the correct…

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Q: 3. Evaluate/calculate using polar coordinates. -1/2 cV1-x² А. M-X" xy/x2 + y² dydx ху,

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Q: Show that the polar equation for x2/a2 + y2/b2 = 1 is                                           r2 =…

A: Plug x=rcosθ and y=rsinθ

Q: The polar equation 9 cos 0 + 2 sin 0 = X + 1 9x + 2y 1 9y + 2x = 1 9x + 2y = x² + y² || || 1 - r in…

A: To find  the cartesian form of the given polar equation.

Q: Given: polar curves C₁ : r = √2- cos 0 and C₂ : r = √2+ sin intersecting at A(³√2, 37) and B(2,7) 2…

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Q: 1. Change to polar form, then evaluate: -x-1 х — у dydx V1-x² /x² + y² -1

A: Solution is given below..

Q: Solve the following Laplace equation in polar coordinates (r, 0). u, 1 du r dr 1 Pu 2 ag2 = 0, for…

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Q: Match the graph with its polar equation. r = 2 sin(0) A/2 л/2 4 2 2 4 A/2 3- A/2 2 -1 2 - 2 -1 1 2

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Q: Given the polar curves: C₁:r = 2 cos 0 ग 2 A(2,0) C2 B(0,0) C₂:r = 2 cos 30 0 The two curves…

A: Any point in the Cartesian coordinate system is represented by the ordered pair x, y. Any point in…

Q: 2 3 4 Identify the coordinates of the point in polar form based upon the given conditions. Use pi…

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Q: 10 Convert the Cartesian equation 2 xy = 1 in polar equation form. r²cos2θ = 0 cosθsinθ = 1/2…

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Q: Replace the Cartesian equation x² + y² equation. OA) r sin² 0 = 4 cos 0 B) r = 4 sin 0 Oc) r = 4 cos…

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Q: Transform C = cos p a, - sin p a, + cos p sin p a, into spherical coordinates and then at P (2, T/4,…

A: Here, we will be transforming C=cos φ aρ-sin φ aφ+cos φ sin φ az into spherical coordinate and then…

Q: A polar equation is given. r = 20/12, os 0 < 41 (a) Express the polar equation in parametric form.…

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Q: 2 3 4 Identify the coordinates of the point in polar form based upon the given conditions. Use pi…

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Q: 2. Identify the coordinates of the point in polar form based upon the given conditions. Use pi for…

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Q: Part A, B, and C

A: According to the given information it is required to sketch the graph of the given polar equation.…

Q: Which of the following gives the Cartesian form of the polar equation r = 7 2cos 0+5sin 0 Select the…

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Q: Match the graph with its polar equation. r = 3 (1 + cos(0)) T/2 1/2 4| -2 2 4 -2 -2 л/2 T/2 3- 2 1…

A: Topic :- Geometry As per our guidelines , In case of multiple different questios ,at a time only one…

Q: Use polar coordinates to evaluate 2/2 dydx. 3 1 0, (x²+y?)? O 5 Оз 6 O 2 O 1 O 4

A: To determine: The value of the integral  using polar coordinates, ∫12∫0x22x2+y232dydx.

Q: . Find a cartesian equation for the given parametric equations: a) x = t2 – 4 and y =t+1 b) x = 2…

A: Eliminating t

Q: Graph z = 4 ( cos +i sin-) on a polar grid. Then express it in rectangular fo COS- 3 12 Y 12 6 12 12…

A: Topic:- coordinate system

Q: Prove that the distance, d, between two points with polar coordinates (r1, θ1) and (r2, θ2) is d =…

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

Q: Solve the following Laplace equation in polar coordinates (r, 0). ²u 1 du 1 Pu + r2 d02 0, for…

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Q: Find two other pairs of polar coordinates of the given polar coordinate, one with r>0 and one with r…

A: Given, the polar coordinates (4, pi/6), we have to find the other two polar coordinates with r &gt;…

Q: 1. Sketch the graph of r = 2 sin(20) in polar coordinate system T/4 31/4 5T/4 7T/4 in the polar…

A: Consider the provided polar equation, Sketch the graph of the polar equation. Now make the graph of…

Q: Q2: Sketch the polar function r 3 6 cos 30 ,-n<0 < m

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Q: Transform C = cos p a, - sin p a, + cos p sin p az into spherical coordinates and then at P (2, T/4,…

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Q: 7. The polar equation of the curve r2 + y² = 2x is A T= 2 cos 0 T= sin 20 T= 2 sin 0 B D T= cos e

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Q: H.W 1-Replace the polar equations with equivalent Cartesian equations 1). r = 2+sin 0 2]. 3]. 4].

A: Given that  r=2+sintheta  To covert the polar equation into Cartesian equation

Q: Convert the polar equation to a rectangular equation. r= 6 cos e + 5 sin 0 О х2 - у2 - 6х + 5y O x²…

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Q: Convert the given Cartesian equation into a polar equation. y = 6x + 3 Select the correct answer…

A: x=rcosθ, y=rsinθ. Use these values to find out result.

Q: Convert the given Cartesian equation into a polar equation. a² +y? - 2x + 3y %3D Select the correct…

A: Put x=rcos thetha and y=rain they ha to get polar equations

Q: Replace the polar equation with an equivalent Cartesian equation. r 2 = 26r cos θ - 6r sin θ - 9…

A: We can make it easier by putting the value of x and y in the equation.

Q: H.W 1-Replace the polar equations with equivalent Cartesian equations. 1]. r = 4 sin 0

A: To convert the given polar equation to Cartesian equation, we make the substitution  x=r cos(θ), y=r…

Q: 3.3. Show that in a polar coordinate system, the distance d between the points (r1,01) and (r2, 02)…

A: The distance between r1,θ1 and  r2,θ2 is d=r12+r22-2r1r2cos θ1-θ2

Q: The Cartesian equation of the polar curve r = 6 sin 0 is (x – 6)² + y? = 36 - (x – 3)² + y² = 9 O a?…

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