Write a polar equation of the form r cos(0 – 0,) = ro for the line 3 x- y = 2.

Q: Write a polar equation of the form r sin(0 – 0,) = ro for the line 2/3 x+2y = 1. %3D

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Q: Write the polar equation in rectangular form. r = 6 sin 0 Oy =-6x Oy =x- 3 O x² + (v – 3)² = 9 O (r…

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Q: Use polar coordinates to calculate e-(z²+y²) dydx. roo Express -(2²+y²) dydx in terms of dr, and…

A: We will find out all the required values.

Q: Convert the polar equation to rectangular form and sketch Its graph. r= 9 sin(@) y y 0.8 0.6 0.4 2…

A: Given: r=9sinθ

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

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Q: 2. Compute [²√x by first changing it to polar coordinates. 1 -√3x (x² + y²) ² dy dx

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Q: Find a polar equation in the form r cos (θ - θ0) = r0 for each of thelines y = -5

A: We need to find the equation in polar form for the given line

Q: Convert the Cartesian equation x² + y² + 3x = 0 to a polar equation. r² = = -3 cos 0 r= 3 cose r= -3…

A: Given x2+y2+3x=0To find polar equation:

Q: 10.4

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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: Convert the Cartesian equation x² + y² -2x= 0 to a polar equation. x2 + y2 -2x 0= O 2=-2 cos e Or= 2…

A: Given artesian equation,x2+y2-2x=0Put…

Q: Find the length of the curve r = 2 sin^3 (u/3), 0 … u … 3pi , in the polar coordinate plane.

A: Given:        r=2sin3u3,  0≤u≤3π

Q: Replace the Cartesian equation with an equivalent polar equation. x² + y² - 4x=0 O A. r cos²0=4 sin…

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Q: Consider the polar curves C1 : r = −3 sin(2θ) and C2 : r = 3 sin θ. 1. What is the equation of the…

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Q: Sketch the curve with the given polar equation. r = 1+2 cos 0 7/2 Зп /4 T/4 2 4 57/4 77/4

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Q: Find the length of the curve r = 2 sin^3 (u/3), 0<=u<=3pai, in the polar coordinate plane.

A: To determine the length of the polar curve.

Q: Consider the curve given in polar coordinates by r = 0 + cos 0 . Compute the slope at 0 = 0. %3D O…

A: Slope of polar curve r=f(theta) is given by dr/d(theta) Differentiating r with respect to theta we…

Q: Find a polar equation in the form r cos (θ - θ0) = r0 for each of thelines √2 x +√2 y = 6

A: Given equation of the line is 2x+2y=6 To change the equation of line to polar equation, we use…

Q: Find the exact length of the polar curve. 4 sin(0), o 0S T/3

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Q: Graph the polar curve r = e® for 0< 0 < n.

A: The given polar curve is,

Q: 9. Sketch the polar curve. r = 2 cos 2 0

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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: Give two polar representations for the point (x, y) = (0, 1), one with negative r and one with…

A: Check the polar representation.

Q: Write a polar equation of the form r cos(0 – 0,) = ro for the line x + y = v2.

A: Given line, x+y=2

Q: Find the exact length of the polar curve. r = e20, o < 0 < 2n

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Q: 9. Sketch the polar curve.r= 2 cos 2 0 ||

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Q: Find the exact length of the polar curve. r = e80, 0 < 0 < 2n

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Q: Show that every line that does not pass through the origin has a polar equation of the formr =…

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Q: Find e-a* -y" dx dy using polar coordinates.

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Q: Find the exact length of the polar curve described by: r = 5e-0 %3D 7 on the interval

A: The given function is r=5e-θ, where  7π2≤θ≤6π. The length of the polar curve is obtained by the…

Q: = Replace the polar equation 8r cos 0 + 9r sin 0 Cartesian equation. OA) 8x +9y = 1 B) 8y + 9x = 1…

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Q: Draw the polar curve to ((x-3)2/32) - (y2/32) = 1

A: We have to draw the polar curves to x-3232-y232=1.

Q: Show that every vertical line in the xy-plane has a polar equation of the form r = a sec u.

A: The relation between polar coordinates r,u and rectangular coordinates x,y is x=rcosu…

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: 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: Convert the polar equation to a rectangular equation. r= 3 cos 0+6 sin 0 O A. 3x+6y 0 O B. x+y 6x +…

A: Recall: Convert form Polar to Rectangular:      x= r cosθ and   y= r sinθ ⇒r2=x2+y2   and  tanθ=yx

Q: xy = 1

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Q: Express the polar equation r=2 sin 0 in cartesian coordirates.

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Q: What is the zero of polar equation r = 3+2cos(θ)?

A: Given polar equation is: r=3+2 cos θ To find the zero of the polar equation, we must have to put θ=0…

Q: Sketch the polar curves r= 9 sin 0 and r 4-9 sin 0. Indicate the co- ordinates of all r and y…

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Q: Convert the point Cr,e)f from polar to nectangular COordinates (xx) 5T 3. ब्लज( कथावक 2)(a,)

A: To convert the given point from its polar form to rectangular form

Q: . Show that the equations x = r cos 0, y = r sin 0 transform the polar equation 1 + e cos 0 into the…

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

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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: b. Plot the polar curve r= 2(1- cos0) in interval t ,2n

A: Given equation is r=2(1-cosθ)  =2-2cosθ

Q: 4. Consider the polar function r(0) = 2+2 cos(20), for 0 E [0, 27). (a) Write parametric equations…

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

A: Given: r=3+5 cosθ We have to sketch the graph of r as a function of θ in Cartesian coordinates…

Q: Find the polar equation for the Cartesian curve ² Or 1 T= cos 2 1 Or=sin @tan 0 2 T = Or= Or T = 1 1…

A: The given cartesian curve x2=y2 we have to find the polar equation

Q: .Find the rectangular equation of the polar curve defined by r = sin 20. A. x+y-2xy= 0 B. (x² + y² }…

A: The polar coordinate system is a coordinate system  in which each coordinate point will be of the…

Q: Write a polar equation of the formr cos(0 – 0) = ro for the line x - V3y = 2.

A: We have to solve given problem: