Show that the polar equation for x2/a2 + y2/b2 = 1 is                                           r2 = b2 /(1 − e2 cos2) .

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: 12/2 Use polar coordinates to evaluate dydx.

A: The region is bounded by x=1,x=2,y=0 and y=x

Q: Find an equation in x and y that has the same graph as the polar equation r- sin 0 = 0 and graph on…

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Q: Find the slope of the tangent line to the polar curve r = cos(30) at 0 = 7. Enter as an integer or…

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Q: 47. Show that every line that does not pass through the origin has a polar equation of the form sin…

A: Let's understand the relationship between polar coordinates and Cartesian coordinates. Please see…

Q: 12/2 Use polar coordinates to evaluate dydx. 3 0. (x² + y²)²

A: To convert cartesian coordinates to polar coordinates , put x=rcosθ, y=rsinθ , dydx=rdrdθ So,…

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

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Q: - A tangent at the pole to the polar curve = V2 – 2 cos0 is 0 = r = A 3

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Q: Find z1z2 in polar form. Z1 = 9 ( cos +i sin 22 = 6 +i sin 4

A: R eiθ=Rcos θ+i sinθ

Q: 9. Transform the equation 2x?+2y?3 into a equa tion. Polar

A: Given

Q: What is y2 = 3x in polar form? r = 3 sin 0 sin 0 O Option 4 r = 3 csc 0 cote Option 2 r = 3 sin 0 -…

A: Given y2=3xTo find polar form:

Q: Draw the polar curve r = cos(30) with its orientation. Set up all integral to evaluate the length of…

A: First, find the node to the polar curve by equating r = 0, so cos(3θ)=rcos(3θ)=0(3θ)=-π2,π2θ=-π6,π6…

Q: Graph the line and conic section. r = 1/(1 + 2 cos u)

A: To graph r  = 11 + 2 cos u.

Q: Sketch a graph of the polar equation. r- -2(1 + sin(0)) n/2 7/2 4. 2 .4 4 -2 2 4. -2 -4 n/2 7/2 4. 4…

A: Given, r= -2(1+ sin theta) Plotting for the given polar coordinates we have,

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

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Q: 1. Change ſ, Lz xy dydx to polar form. 4-x2

A: We will answer the first question as we don't answer multiple question at a time. Please resubmit…

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: 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: = 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: 8 Convert the polar equation r 2 = -2 sin 2θ to a Cartesian equation. x2 + y2 = 2 xy ( x2 + y2) 2…

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Q: 5. If z = 2(cos 25° +j sin 25°), find z in polar form.

A: It is simple calculation in polar form

Q: 2. Express in true polar form, z 5(cos 55°-j sin 55°)

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Q: Find the slope of the line tangent to the following polar curve at the given point. 3π r= 5-5 sin 0;…

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Q: Into polar coc x2 + y² = 3x %3D

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Q: •5 25-x2 Evaluate (x² + y? )° dy dx by converting to polar coordinates.

A: To evaluate the integral using polar coordinates

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: compute the length of the polar curve. r = cos2 θ

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Q: The x- intercept of the tangent line to the polar curve r=3(1+sin 0) at 0=" 프 is

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Q: Find the length L of the polar curve r = 6 sin for 0 < 0 <- 2 2 OL= 12 OL= 6 OL = 6/2 OL = 12 – 6/2

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Q: Compute the length of the polar curve 702 for 0 s 0 < 4.

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Q: Calculate the length of the polar curve r=1- sin Oon the given interval (0, 2m].-

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Q: 8 sin ( *(4) in the interval 0 < 0< . Calculate the length of the polar curve r =

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Q: Find the equation in xx and yy for the line tangent to the curve in polar coordinates…

A: Given that, the value of r=5+cos2θ and θ=π3. rθθ=π3=5+cos2π3=5+-12=92 Note that, the equation of the…

Q: 44. The furthest point from the pole to the polar curve r = 2+ V2 sin 0 occurs when 0 = A. в о C 2

A: Answer

Q: Determine the Cartesian equation of the tangent line to C1 at the point where 0 = π/2. Given: polar…

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Q: 1. Find two sets of polar coordinates for (x, y) = (-V3,1, one with r> 0 and one with r< 0, both…

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Q: Find the slope of the tangent line to the given polar curve at the point specified by the value of…

A: Given and

Q: Consider the curve. (금) 2 = 1 19 + Identify all possible parametric equations for the given curve. O…

A: In this question, we can check one by one parametric equation in the given curve.

Q: A particle moves along the polar curve r =1– 2 cos 0 so that = 2. Find the value of d at e = , and…

A: We are given that,                     Now,              When          , Then

Q: Give an example of two polar equations, r1(0) and r2(0), whose graphs intersect in at least two…

A: According to the given information, it is required to give an example of two polar equation whose…

Q: What is (x - 12)² + y² = 144 in polar form? r = 24 sin 0 r= 24 cos 0 O Option 1 r= -24 sin 0-144…

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Q: 3) Use polar coordinate to evaluate S'S_√x² + y² dxdy.

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Q: 4. Draw the polar curve defined by r= 3 –2 cos 30.

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Q: Find the slope of the tangent line to the given polar curve at the point specified by the value of…

A: The given polar curve is,

Q: A Find a polar equation for 1. (x - 3)2 + (y + 1)2 = 4. 2.x2 + xy + y? = 1

A: Find a polar equation for  ( x -3)2 + (y+1)2 = 4 and x2 + xy + y2 = 1. Here i provide full solution…

Q: Sketch a graph of the polar equation. r= sin(40) T/2 オ/2 1.0 1.0 -1.0 0.5 1.0 -1.0 -0.5 0.5 1.0 -0.7…

A: Given that r=sin(4θ) Here my objective to sketch a graph of given polar function.

Q: Find the slope of the tangent line to the given polar curve at the point specified by the value of…

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Q: a. Find the solution set for log, 2+2.log3 x= log, (7x-3) b. Plot the polar curve r 2(1-cose) in…

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

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