10. Given the polar equation r = cos gi a) find the eccentricity, b) identify the conic form, c) give an equation of the directrix(s), and d) sketch a graph indicating the vertices and foci.

Q: Find the eccentricity, identify the conic, and equation of the directrix. 1 r = 2 + sin 0

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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: identify the type of conic, the eccentricity, and the equation of the directrix. r = 8/1 + 4 cos θ

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Q: Given the polar equation of the conic with focus at the origin, identify the eccentricity and…

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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: 2 The rectangular cererdinates of a paint are given as (-4, -3) . Find the polar courding tes for…

A: We know that in 2 dimensions a point in its polar coordinates is given by   (rcos(θ),rsin(θ)). Thus…

Q: Cannot solve

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Q: 5 equally spaced holes on an 80mm pitch circle diameter. Calculate their co-ordinates relative to…

A: we know that, the total sum of angles in circle= 360 so now using this we will solve the question.

Q: Find a polar equation in the form r= f(θ) of the ellipse with eccentricity e= 6/7 such that one of…

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Q: Identify the conic the polar equation represents and give the position of the directrix. 1 1-sin 0…

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Q: Graph the line and conic section. r = 8/(1 - sin u)

A: We can convert this into rectangular form. Then,…

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

A: Use the formula: x=rcos (u), y=rsin (u), x2+y2=r2   r (1 + 2 sin(u)) = 1r + 2r sin(u) = 1   Thus…

Q: Find a polar equation in the form r= f(θ) of the hyperbola with eccentricity e= 4 such that one of…

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Q: In polar coordinates, r is the ________ ________ on the terminal side of an angle uwhose vertex is…

A: The given statements is "In polar coordinates, r is the ________ ________ on the terminal side of an…

Q: Write a polar equation in rand of an ellipse with the focus at the origin, with the 8 eccentricity…

A: A polar equation  of the form r=ed1±e cosθ, r=ed1±e sin θ represents a conic with eccentricity e…

Q: Give the eccentricities of conic sections with one focus at the origin of the polar coordinate…

A: Solution:- Eccentricities of conic is, e=1 Directrix is  r cos u=-4 That is, x=-4 Now polar…

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: Write the name of the conics giver by poloar curve r=6/(2+sin(t)) a) Determine the vertices in the…

A: We need to write the name of the conics given by the polar curve r=6/(2+sin(t)). Also, we need to…

Q: 4. Find the distance from the pole to the vertices, and then find the equation of the ellipse in…

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Q: Write the name of the conics given by polar curve r=6/(2+sin(t)) a) Determine the equation of the…

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

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Q: Identify the conic that the following polar equation represents. 5 r = 10 + 5 sin 0 Select the…

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Q: Identify the conic that the following polar equation represents. 8 r = 2+2 sin 0 Select the correct…

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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: 3 Identify the conic represented by the polar equation r 1 Find the rectangular equation. 2 cos 0

A: Given equation, r=31-2cosθ                              ....(1)

Q: Work out the product of 2cos60° x 3cos30° in polar and rectangular form.

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Q: 10. Given the polar equation r = , a) find the eccentricity, b) identify the conic form, c) give an…

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Q: Calculate the distance around the graph of the polar curve r = 3sin 0. O 67 o 37 O 16

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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: Given a pair of parametric equations x = 2 cos(t) – 4 and y = 3+ 3 sin(t). i. Eliminate the…

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Q: r = 2– sin(0)"

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Q: Consider the curves: r = 4sin 0 and r = 2 sin(0) + 2cos (8). a) Sketch a graph of both curves on the…

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Q: What kind of the polar graph has the equation r = 2 + 2 cos 0? limacon cardioid lemniscate…

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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: 4 4. a) Identify the conic section given by the polar equation and also determine 1-cos e its…

A: We convert the equation into rectangular form first This is a parabola.

Q: 11. Write a polar equation of a conic with the focus at the origin given the following:…

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Q: 4. Sketch a clear and accurate graph of the polar equation r 1-2cos 0.

A: To sketch a clear and accurate graph of the polar equation r=1-2cosθ Here r is the distance from the…

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

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Q: Consider the rose curve with polar equation r = cos(20), whose graph is shown below. 0.5 -0.8-0.4서…

A: An integral assigns numbers to functions in a way that describes displacement, area, volume, and…

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: For the given polar curve, identify the conic, find the equation of the directrix, and sketch it: r…

A: Given: The function is given as ? = ?/?+?????

Q: Give the equation in polar coordinates of a conic section with a focus at the origin, eccentricity…

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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: While playing at the Nawaka Sevens, four of the rugby players are observed to be located at the…

A: The derivative is defined as the rate of change of one quantity with respect to another. In order to…

Q: Sketch the graph of the polar equation.r = 2θ, θ ≥ 0 (spiral)

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Q: Exercises 19–22 give the eccentricities of conic sections with one fo- cus at the origin of the…

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Q: Convert the given polar equation to a Cartesian equation. r= 6.cos(e) In Cartesian, this equation is…

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