a) Show that the polar equation r = a sin 0 + b cos 0, where ab # 0, represents a circle. Find its center and radius. b) Show that the curves r = a sin 0 and r = a cos 0 intersect at right angles.

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: 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: r = -4 sin 0,

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Q: Sketch the polar curve r = cos(20) COS

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Q: a) Reproduce the algebra required to convert this Cartesian equation to the polar form r = sin(20).…

A: Given the algebraic equation, (x2+y2)3=4x2y2 ⋯⋯(1) (a) Take x2+y2=r2, x=rcosθ, and y=rsinθ Then…

Q: Consider the conic section given by the polar equation 4 1-sin 0 r=

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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: 2. Convert the polar equation r = cot 0 csc 0 to rectangular form and sketch its graph.

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

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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: Sketch the graph of the polar equation.r = 1 + 2 cos θ

A: Consider the provided polar equation, r=1+2cosθ Sketch the graph of the polar equation. Now make the…

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

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Q: (a) Rectangular coordinates of a point (x, y) may be recovered from its polar coordinates (r,θ)by…

A: We know, Polar coordinate (r,θ) and rectangular coordinate (x,y) are related as follows:…

Q: Determine the points at which the limacon defined by the polar equation r = 3+ 2 sin 0 has…

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Q: Find a polar equation for the curve represented by the Cartesian equation: x² = 8y. Or= 8 sin cos 0…

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Q: Sketch a graph of the polar equation and find the tangents at the pole. r = 3cos2θ

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Q: 9. Sketch the polar curves r = 5sine and r = 5 sin(30) on the same grid below.

A: The given polar curves are  r=5sin(θ)r=5sin(3θ)

Q: If a point is represented as (x,y) in the Cartesian plane and (r,0) in the polar plane, then 0 = tan…

A: A point in cartesian plane is (x,y) and (r,θ) in the polar coordinate, then θ=tan-1yx.

Q: 6. Find a Cartesian equation for the polar curve and describe its shape: r= 3csce

A: The given equation,              r=3 cscθ

Q: Write in Polar form: r(cos 0 + i sin 0). (0 < 0 < 2n and round to 3 decimal places) – 12 – 3i r = ,…

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Q: Find the area and circumference of the circle represented by the polar equation r = 6 cos 0 using…

A: The given problem is to find the area of circle and circumference of the circle for the given circle…

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

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Q: Show that the polar equation r = asin(θ)+ bcos(θ), where ab≠0, represents a circle, and find its…

A: We have to proof

Q: Find the areas of the regions in the polar coordinate plane described Enclosed by one leaf of the…

A: Area of the region bounded by r=fθ between the radial line α to β is A=12∫αβr2dθ

Q: find the area of the polar curve.   r=3-sin@

A: To calculate the area of the given polar curve , using integration

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

A: Polar equation r= -3 cosθ , -π≤θ≤π

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

A: Given: r = 2 sin 4θ

Q: Convert the following polar curves into Cartesian r=2/(4-cos theta)

A: We know that--&gt; r2 = x2 + y2  x = rcosθ y = rsinθ

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

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Q: Consider the polar curve r = sin(30). Sketch the polar curve on the inter 0< 0 < 27/3.

A: Solution: Given data, r = sin(3theta)

Q: Sketch the graph of the polar equation.r = 2 - cos θ

A: We need to sketch the graph of the polar equation.

Q: Find the exact length of the polar curve. 3 sin(0), 0 < 0< 1/2

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Q: Replace the polar equation with an equivalent Cartesian equation.  7r cos θ + 9r sin θ = 1

A: Answer is mentioned below

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: Which of the following polar equations describes a circle centered at (G, 5) with radius 2 O r =…

A: Given, center=(12,12) radius=12

Q: Plot the graph of r= sec 0 tan 0.e a b Find the Cartesian equation corresponding to this polar…

A: Polt the polar curve and conversation of polar coordinates

Q: Sketch a graph of the polar equation and nd the tangents at the pole. r = 3 (1 − cosθ)

A: By using polar curve

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

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Q: 4. Consider the point with rectangular coordinates (1, 1). State the coordinates of the point in…

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Q: Sketch the polar curve with the given equation "= -4 cos 0, - TSOST.

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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: 1 r = sin 0-4 cos 0

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Q: Which of the following is one of the points of intersection of the polar curves r = 3 cos @ and r =…

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Q: Sketch the polar curve with the given equation - -3 sin 8, OA OB. oc OD. OE

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Q: 7. What is the equation of the curve in rectangular coordinates whose equation in polar coordinates…

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Q: Sketch a graph of the polar equation r = 3 cos 4θ and find the tangent lines at the pole.

A: Given: The equation r=3 cos 4θ To sketch: The graph of the given equation. To find: The tangent…

Q: 10 Write an equivalent rectangular equation for the polar equation r = 3 sin 0-7 cos 0

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Q: Show that the polar equation r = a sin θ + b cos θ where ab ≠ 0 represents a circle, and find its…

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Q: Sketch the polar graphs and find the points of intersection for the curves: r = sin(θ) and r =…

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