A curve with polar equation r=39/9sin(x)+64cos(x) represents a line. This line has a Cartesian equation of the form y=mx+b,where m and b are constants. Give the formula for y in terms of x. For example, if the line had the equation y=2x+3 then the answer would be 2⋅x+3

Q: r = 2 cos 0,

A: To find the exact length of the polar curve.

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: Find the slope of the line tangent to the polar curve at the given point. 9 11t r= 9 sin 0; 2' 6

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Q: Find the slope of the polar curve at the indicated point. TT 7) r = 5 cos 30, 0 =

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Q: Find the exact length of the polar curve r=1+ cos 0

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Q: find a polar equation for the curve represented by the given cartesian equation 5x^2 +y^2 = 8x (r is…

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Q: Find a polar equation for the curve represented by the given Cartesian equation.

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Q: Find a polar equation in the form r cos (0 - 0) = ro for the line x = - 12.

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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: Sketch the curve with polar equation r = 2 cos0

A: We first make a table of values θ 0 π/4 π/2 3π/4 π r 2 1.41 0 -1.41 -2

Q: Consider the curve C of equation (2x² – y + y³)² = a² + y? From the choices given, select the one…

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Q: The polar equation r = a+a cos 8, where a > 0, has a tangent line at (0, 7)

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Q: Find the slope of the line tangent to the polar curve at the given point. 11n r= 4 sin e; - 2,-

A: Given,            r=4sinθ ; -2,11π6

Q: Find a polar equation for the curve represented by x2 + y2 = 8cx, where c is a constant.

A: The given equation is x2 + y2 = 8cx   Known fact x=rcosθy=rsinθ

Q: Find a polar equation in the form r cos (0-0) = ro for the line 2/2x+2/2 y = 16.

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Q: Find the exact length of the polar curve. r=4 sin(θ), 0<θ< π/2

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

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

A: Given: To find the polar equation of the form r cosθ-θ0 =r0 for the line 3x-y = 2.

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 a polar equation for the curve represented by the given Cartesian equation. x² + y2 = 16

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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 Find the Cartesian…

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Q: A curve with polar equation r = 8 sin 0 + 49 cos 0 represents a line. This line has a Cartesian…

A: The polar equation is, r=58sinθ+49cosθ   Rewrite the equation. 8rsinθ+49rcosθ=5   Substitute y for…

Q: Find the equation of the line tangent to the polar curve at the point. r= 2cos(θ/ 3),  θ =π/4

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Q: Find the exact length of the polar curve

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Q: Find the exact length of the polar curve. = 02, 0s0 < T/2

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

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Q: 4. Find a polar equation for the curve represented by the Cartesian equation y = 3x. T = r cos 0, y…

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Q: Find a polar equation for the curve represented by the given Cartesian equation. x2 + y2 = 10cx

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Q: 33 A curve with polar equation r 9 sin 0 + 55 cos 0 mx + b,where m and b are represents a line. This…

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Q: A curve with polar equation r = 20 4 sin 0+ 17 cos 0 represents a line. This line has a Cartesian…

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Q: 1 r = sin 0-4 cos 0

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Q: 36 r= e®,-π <θ <T

A: Consider a function f such that its derivative is continuous in the interval α≤θ≤β. Then the length…

Q: Consider the curve C of equation 4.xy x² + y? x² + y² From the choices given, select the one that…

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Q: b, The polar equation for the curve whose rectangular(cartesian)equation xy32 is: (a)rcosesine = 4 4…

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Q: Sketch the curve with the given polar equation, and find its Cartesian equation. 2 =-4 sin 20 %3D y

A: We are given the polar equation . Let us plot the figure.

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: Find the length of the curve over the given interval. Polar Equation Interval r = 8a cos 0 16 16.

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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: 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: Replace the Cartesian equation with an equivalent polar equation. xy = 1

A: Consider the equation  xy=1

Q: Find a polar equation for the curve represented by the given Cartesian equation. xy = 6

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Q: Find the polar equation for the curve represented by the equation y = 1+ 3x. A 1 ,0) sin 0-3 cos 0 В…

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Q: Find a polar equation for the curve represented by z +² = 8cz, where e is a constant.

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Q: onvert the given Cartesian equation to a polar equation. (Use the following as necessary: r and 0.)…

A: Explanation and solutions is given below.....

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:

Q: Find the exact length of the polar curve described by: r = 7e-0 3 on the interval 10

A: r=7e-θ,    310π≤θ≤6π Differentiating with respect to θ, we get drdθ=7-e-θ=-7e-θ

Q: A curve with polar equation 32 3 sin 8 + 13 cos e represents a line. This line has a Cartesian…

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Q: 23 A curve with polar equation r : 4 sin 0 + 13 cos 0 represents a line. This line has a Cartesian…

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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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