What is the polar equivalent of the equation of a circle with center on the y- axis, radius equal to 2 and passing through the origin? A. r= 2+2 sin e B. r 2 sin e C. r= 4 sin 0 D. r=4cos0

Q: Find Cartesian equation for the circle. Sketch circle in the coordinate plane and label it with both…

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Q: Find the exact length of the polar curve. r= theta, 0<= theta <= 3(pi)/4

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Q: The following polar equation describes a circle in rectangular coordinates: T=8 cos 0 Locate its…

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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: Q1) Find the polar equation of the circle whose center has polar coordinates (a, 6,) and radius a.…

A: We will solve the problem.

Q: 2 -   If the center of the circle given by the equation r = 6sinθ – 8cosθ in polar coordinates is…

A: As we know that the polar coordinate is: x=rcosθ,y=rsinθr=x2+y2 Given: r=6sinθ-8cosθ So, we can…

Q: What is the radius of the circle for the polar equation r = 15 cos 0? Enter a numerical value only,…

A: Converting from polar coordinates to Cartesian coordinates.

Q: The following polar equation describes a circle in rectangular coordinates: r = 4 sin 0 Locate its…

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Q: The polar equation for the curve whose rectangular(cartesian) equation xy = 4 is: (a)rcos@sin0 = 4…

A: Explanation of the answer is as follows

Q: Find a rectangular equation of the portion of the cycloid given by the parametric equations x = a(θ…

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Q: Find the equation of the tangent line to the circle r=4cos(t) at the point where t=PI/6. (a)Also…

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Q: Find the circumference of a circle described by the parametric equations = 7 cos 0 and y = 7sin 0…

A: The formula L=∫dxdθ2+dydθ2dθ is formula for length of arc in polar coordinates. As we go along the…

Q: 1. Consider the rectangular (Cartesian) equation x? + (y – 2)² = 4. - d. Choose one point on this…

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Q: Which of the following polar curves is a cardioid? A. r= cos ? () B. r=2+3sine C. r= 3- 2 cose D. r…

A: Use the standard form of polar equation of cardioid and compare with the given options.

Q: Change the following from polar points (r, theta) to rectangular points (x,y). a)     (5,150o) b)…

A: We know that polar coordinates (r, theta)  and rectangular coordinates (x,y) are related by the…

Q: 13 The polar equation r = 2/7 sin0 + 6cos0 represents a circle with radius (a)V7 (b)4 (c)3 (d) 16…

A: The given equation is; r = 2√7 sin(theta) + 6 cos(theta)

Q: The letters x and y represent rectangular coordinates. Write the given equation using polar…

A: Using relationship between rectangular and polar coordinates ,

Q: Find the lengths of the curves given by the polar coordinate equations r = 8 sin3 (θ/3), 0≤ θ ≤ π/4

A: Given data: The polar coordinate equation is r=8 sin3(θ/3). *The limit of the function is 0≤ θ ≤…

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Q: Find a polar equation for the curve represented by Cartesian equation x? = 22y. O A.r = 44 tan 6Osec…

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Q: e = 2 / 3; directrix is parallel to the polar axis, 3 units above thepole.

A: Given e = 23 &lt; 1  Hence the given conic is ellipse.

Q: 2. Use polar coordinates to evaluate √9-1² 2 L √4+x² + y² dy dx.

A: This is a problem related to integral of polar curves. Based on the substitution in cartesian…

Q: A) Use polar coordinate system to sketch and find the area in side r = 8 cos0 out side x? + y? = 16.

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Q: Show that the graph of the equation r=2a cos θ,a&gt;0, is a circle of radius a with center at (0,a)…

A: Given: r=2a cos θa&gt;0

Q: The polar equation of the circle with Cartesian equation x² + y2 = 100 is:« A r= 100- В r= 10 sin 0…

A: To find  The polar equation of the circle with the given equation.

Q: The polar equation for the curve whose rectangular(cartesian)equation xy = 2 is: (a)rcosesine = 4…

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Q: Find the distance between the following points wchich are represented in polar coordinates, P: (r,…

A: Given query is to find the distance between given points.

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: 22. y dA, where S is the first quadrant polar rectangle in- side x? + y? = 4 and outside x+ y? = 1

A: Evaluation of the double integral by using polar coordinates

Q: Which of the following statements is true for the polar equation r + 6 sin 0 = 0? A. It represents a…

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Q: Determine in polar coordinates the center and radius of the circle r2 + 4r cos(θ) − 4√3 r sin(θ) −…

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Q: all parts need in separate separately.

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Q: Find a polar equation for the curve represented by Cartesian equation x? = -13y. O A.r = 169 sin…

A: Given cartesian equation  x2=-13y We have to convert it into the polar equation.

Q: Use the Distance Formula to find the distance between the two points in polar coordinates. (Round…

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Q: Tind the exact length of the polar curve re 2cos g unere

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Q: Mark the alternative that corresponds to the radius R and the center C (in polar coordinates (r,θ))…

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Q: Which polar equation produces a Spiral of Archimedes? 13. С. r sin e = 2 A. r cos e = 2 P. D. r= 20

A: Here we have to find the polar equation which produces a Spiral of Archimedes.

Q: Q1) Find the polar equation of the circle whose center has polar coordinates (a, 0,) and radius a.…

A: Given a polar point (a, theta 0) and radius a.

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 point that has the given polar coordinates. (2, ) R/2 R/2 T/?

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Q: O E What is the polar equivalent of the equation of a circle with center on the y- axis, radius…

A: Polar equation of circle is define by : x2cos2θ+y2sin2θ=r2 . co-ordinates are xcosθ , ysinθ and r is…

Q: Find the lengths of the curves given by the polar coordinate equations r = 2 sin θ + 2 cos θ, 0 ≤ θ…

A: Given: r=2sinθ+2cosθ; 0≤θ≤π2 for finding length of curve given by the given polar equation, first we…

Q: The polar equation r = 2/5 sino + 4cose represents a circle withradius (a)V5 (b)9 (c)3 (d) 6 (e)…

A: 1.Convert from polar form to cartesian form 2.Compare it with equation of circle in cartesian form.

Q: Which of the following is a Cartesian equation for the curve given in polar coordinates byr 3? %I a.…

A: x = r cos(θ) y = r sin(θ)

Q: Find the Cartesian coordinates of the given polar coordinates. a) (4,pi) : (x,y)=? b) (4, -2pi/3)…

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Q: the center of the circle given by the equation r = 6sinθ – 8cosθ in polar coordinates is M(a, b) and…

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Q: Consider the following. x = cos ? + 1,    y = sin ? − 2;    0 ≤ ? ≤ 2?   (a) Find a rectangular…

A: The parametric curves x=cost+1 and y=sint-2. o≤t≤2. We have to answer the following...

Q: The following polar equation describes a circle in rectangular coordinates: r = 14 sin 0 Locate its…

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Q: Find a polar equation for the curve represented by the given Cartesian equation. 9. a? + y? = 25

A: Given equation x2 + y2 = 25 To be found : Polar form.of given equation.

Q: True or False: When you test a polar equation for symmetry and you find out that it is symmetric…

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