Which of the following equations represents the subset of the xy-plane with polar description r = 4 cos 0? (x – 2)? + y? = 4 (2 – 4)? + y? = 16 None of these. æ² + (y – 2)? = 4 x? + (y – 4)? = 16

Q: CONVERT the below graph in the xy-plane TO a graph in the polar plane FOR ONLY the interval A/2 2' 2…

A: TO convert a graph from xy plane to polar plane we need to find points on the graph  from the xy…

Q: 2 7 Find the projection of v = -1 onto the line tlof R'Igiven by the parametric equation e = tul…

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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: Show that r = fi(0) and r = f2(0) define the same curves %3D in polar coordinates if f1(0) = – f2(0…

A: Given, r=de1-ecosθ, r=-de1+ecosθ define same curve r=f1θ=f2θ show that  f1θ=-f2θ+π…

Q: Consider the polar curves C₁ : r = 2 cos 0 and C2 : r = 2 cos 30, and let R be the shaded region as…

A: Given: C1:r=2cosθC2:r=2cos3θ To find: Area of the region

Q: 6. Find the projection of v = | -7 onto the -2 line l of R given by the parametric equation l = tủ,…

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Q: the xy-plane, centered at the origin, oriented clockwise so that the point (5,0) corresponds to t =…

A: we have to find parametrization of circle.

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: Find the length of the polar curve r = 13 sin 0, 0s es 2n - O A. 65 % %3D O B. 26 % O C. None of…

A: Length of the curve r=f(θ) for a≤θ≤b is given by L=∫abr2+r'2 dθ Here r=13 sinθ, 0≤θ≤2π ⇒a=0,…

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

A: To determine the length of the polar curve.

Q: Which of the following is the parametric equation of the line through the point (1,2,3) and parallel…

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Q: 8. The position of a particle moving in the xy-plane is given by the parametric equations x =…

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Q: Q2 (a) A curve C has a polar equation of r = tan 0,0 < 0< 2 Find a Cartesian equation of C in the…

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

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Q: The parametric equations that correspond to T= (2t 1) i- 3vtj+ sin 3t k is %3D

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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: Find a set of parametric equations for the graph of y = 4x² + 2 using the parameter t = x – 3 O x =…

A: Given parameter- t=x-3 Then,  x=t+3

Q: 4. Use the polar graph for the following */2 2n/3 3n/4 5n/6, 7n/6" 5a/4 71/4 4n/3 ŠR/3 3n/2 d)…

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Q: Find the exact length of the polar curve described by: r = 8e 3 on the interval a <o< 9n. 2"

A: The length of a polar curve r=fθ in the interval α≤θ≤β is given by L=∫αβfθ2+f'θ2dθ. The given curve…

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: Q.3) Use the polar coordinates to evaluate A) L (r+ 2y) dydz

A: In this question we have to evaluate the Double Integration in polar form.

Q: Find the exact length of the polar curve described by: 0 r = 4e 5 on the interval 6 ≤0 ≤ 6.

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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: 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: Prove that the distance, d, between two points with polar coordinates (r, 01) and (r2, 02) is d =…

A: Distance (d) between two points x1, y1 and x2, y2 is  d=x1-x22+y1-y22   ....1

Q: Which of the following is the parametric equation of the line through the point (1,2,3) and parallel…

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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: 3) (a) Find the intersection points of the polar curves r = 3 + 2sin0 and r = 2

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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: Find the exact length of the polar curve described by: r = 9e-0 5 on the interval -T <O<67. 6

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Q: Which of the following is the distance from point. A( V5, 0) to point B(2V10, Y) in polar…

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Q: 17. Consider the following parametric equations. x = Vt + 4, y = 3VE, , 0st < 16 a. Eliminate the…

A: The given data is: x=t+4       ....1y=3t          .....2 0≤t≤16

Q: 1/a- Find the parametric equation of the line passing through Po(1,3,4) parallel to 21-j+5k b- Find…

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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: Consider the graph of a polar curve in the r0-plane plotted only from 0 = 0 to 0 = 27/3. Plot this…

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Q: 2. Consider the polar curve r = 0² + cos(0) where 0 < 0 < 5. Which of the following values of 0…

A: note : in polar coordinate r=k , where k is a constant , represents a circle of radius k centered at…

Q: Find a parametric representation = z(t) for the upper half of = Z Iz – 4+ 2i| = 3.

A: Given to represent parametrically z=zt for the upper half of  z-4+2i=3 Let z=x+iy Then the equation…

Q: 12. Let # be the intersection of the planes 2g-ytz30 and a-2y+2=0 in R³ Find parametric equations…

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Q: 7. Find the exact length of the polar curve: r= 0² , 0<0<2T

A: We will use following formula to find Length of the polar curve  integrationr2+drdθ2dθ

Q: Find the length of the curve r= /1+ cos 20, 0<0<n/2/6. The length of the polar curve is.

A: We know the arc length formula for polar coordinates is L=∫θ1θ2r2+drdθ2dθ. Here, r=1+cos(2θ),…

Q: Consider the conic below a2 + 4xy+4y² – 2/5x + V5y = 0 and determine what is asked. 1)…

A: If we have a rotated conic with the general equation: Ax2 + Bxy + Cx2 + Dx + Ey + F = 0, then, we…

Q: Which of the following is the length of the polar curve r = 0 , 0<0 <1? V2 – In (v2+ 1) 2 V3 – In…

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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: 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: 1 If the parametric equatioms are: x= sin-t and y= cos,t, 1 %3D - nstSn 2 then the Cartesian…

A: Given x=sint2, y=cost2, -π⩽t⩽π

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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Q: 6. Find the projection of u = -7 onto the -2 line e of R given by the parametric equation l = tũ, -1…

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