(b) Convert the polar equation, r – 6r cos(0) + 9 = 16 into rectangular (Cartesian) coordinates.

Q: Find the Cartesian equation of the polar equation p² = 2[1+ r(cos 0 – sin 0)] and identify its…

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Q: Replace the polar equation with an equivalent Cartesian equation. r 2 + 2r 2 sin θ cos θ = 576

A: Given: r2+2r2sinθ.cosθ=576 Solution: By taking common r2 we can write above equation,…

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: Transform the polar equation r = 3 sin(0) to an equation in x and y. %3D

A: Converting the polar equation to rectangular equation

Q: 11) Find the rectangular form of the polar equation: r = sin 0 + cos 0

A: Given: r = sin θ + cos θ To find: The rectangular form of the given polar equation.

Q: Find a polar equation that has the same graph as the equation in x and y.(x - 1)2 + y2 = 1

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Q: 24/ Replace the polar equation r. sin (0 +") = 2 to Cartesian equation -(G+ ns./ = 2

A: The given polar equation is r·sinθ+π6=2 .................(1)

Q: Sketch the graph of the polar equation.r = 2 + 4 sin θ

A: Given polar equation is r=2+4sinθ

Q: Sketch a graph of the polar equation  r = −3 cos 2θ

A: We will make a table for the function.

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: convert the cartesian equation to a polar equation x2-y2=1

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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: Sketch a graph of the polar equation  r2 = 9 cos 2θ

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Q: Use the identity cos 2θ = cos2 θ − sin2 θ to find a polar equation of the hyperbola x2 − y2 = 1.

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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: Sketch the graph of the polar equation.r = 3(1 + cos θ)

A: To sketch the graph of r=3(1+cos θ), use Desmos graphing calculator and label the axes.

Q: Convert the rectangular equation x2 + y2 = 16 to a polar equation that expresses r in terms of θ.

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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 rectangular equation x2 = 6y to a polar equation that expresses r in terms of θ.

A: The given equation is:

Q: Identify the conic section and graph the polar equation: r = 2/(1 - cos θ)

A: The given polar equation is r=21-cosθ Here, the given equation can be ellipse, parabola and…

Q: Convert the rectangular equation x2 + y2 = 9 to a polar equation that expresses r in terms of θ.

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Q: Convert the polar equation r² = 2 cos (-20) to a Cartesian equation. (x² + y²)² = 2x²-2y² (x² + y²)²…

A: In this question, we want to convert the polar equation in Cartesian equation.

Q: Sketch a graph of the polar equation r = 5 − 4 sin

A: The given equation is r=5-4sinθ. Sketch the graph of the above equation as shown below.

Q: Convert the equation r2 = -4r cos θ from polar to cartesian.

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Q: Convert the polar equation to rectangular form. 4 r = - 1 - cos 0

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Q: Find a polar equation corresponding to the given rectangular equation. y= 15 1 sec(0) r= 15csc(0) r=…

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Q: Write a polar equation of the form r sin(0-00) = ro for the line 3 x + y 1. 2mark dentify and draw…

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Q: Convert the rectangular equation (x - 1)2 + y2 = 1 to a polar equation that expresses r in terms of…

A: We have to convert the rectangular equation x-12+y2=1 to a polar equation that expresses r in terms…

Q: ) Identify the conic section given by the polar equation r =

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Q: Convert the polar equation, r – 6r cos(0) + 9 = 16 into rectangular (Cartesian) coordinates.

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Q: Sketch the graph of the polar equation.r2 = 4 cos 2θ (lemniscate)

A: The polar equation is,r2=4 cos 2θ

Q: Sketch the polar curve with the given equation = -3 cos 0,

A: Polar equation r= -3 cosθ , -π≤θ≤π

Q: 1. Convert from a rectangular equation to a polar equation. X-y= 10

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Q: Consider the polar equation of a conic. Determine the eccentricity. -5 r = 1 + cos(0) e =

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Q: Sketch the graph of the polar equation.r = 2 sin 4θ

A: Given: r = 2 sin 4θ

Q: 5. Find the Cartesian form of the polar equation: r sin 0 = In(r cos 0)

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Q: Sketch the graph of the polar equation.r = 2(1 + sin θ)

A: To find : sketch graph of  r = 2(1 + sin θ)

Q: 2) Sketch the graph of the curve with the polar equation: r= 2– sin(20).

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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: Convert the polar equation of a conic section to a rectangular equation. 8 r = 7 - 3 cos(0)

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Q: Convert the polar equation r- 3 cosa 5 sin A in Cartesian equation form. )x² + y² - 3x = 5y 1- 3x =…

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Q: Convert the given polar equation into an equation in terms of Cartesian coordinates.

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Q: Sketch the graph of the polar equation.r = 5 + 3 sin θ

A: The given polar equation is r=5+3sinθ. Substitute…

Q: 2. Convert from a rectangular equation to a polar equation. x = 2y2

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Q: Convert x=3y+1 into a polar equation.

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Q: Convert the polar equation to rectangular form. 8 r = 1 - cos 0

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Q: Convert the polar equation to rectangular form. r = 1 - cos 6

A: Find rectangular form

Q: Sketch a graph of the polar equation r2 = 4 cos 2

A: Given:       r2=4 cos2θ First, notice that             r2=4 cos2θ⇒4 cos2θ=2cos2θ Applying following…

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: