EXAMPLE 8 Conics in polar coordinates Use a graphing utility to plot the curves e with e = 0.2, 0.4, 0.6, and 0.8. Comment on the effect of varying the 1 + e cos 0' eccentricity, e.

Q: 14 Sketch a graph of r Use the graph to write a Cartesian equation for the conic. %3D 3 – 4 cos(8)

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Q: 50. Challenge Problem Suppose that a conic has an equation ep of the form r = If the polar…

A: A polar coordinate is of the form (r,θ) where r is the radius and θ is the angle made by radius with…

Q: 5. (a) Find the constants a,b,c for the conic r=- Sketch the conic. 5+sin A

A: A conic equation can be represented using a polar equation. There are various types of polar…

Q: (a) Sketch the curve C1 with polar equation r 2 sin 0. (b) Let C2 be the curve with polar equation r…

A: We have to sketch the curve C1 with a polar equation r=2sinθ. Also, find the intersection points of…

Q: 36 Sketch a graph of r = Use the graph to write a Cartesian equation for the conic. 4 + 5 sin(0)

A: Sketch the graph of r=364+5sinθ as shown below.

Q: What conic does the polar equation r = 2/(1 + cos u) represent? Graph the conic

A: The given polar equation is Since, the cartesian coordinate(x,y) for the polar coordinate is given…

Q: 3 2+ sin 0 equation of the conic in rectangular coordinates. Sketch the conic. Given r=- Find the…

A: Given equation of conic is r=32+sinθr=1231+12sinθ Distance of vertices from pole =3 We know that…

Q: Determine the eccentricity & type of conic ;write an equation of the directrix corresponding to the…

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Q: 18 Sketch a graph of r .Use the graph to write a Cartesian equation for the 5+ 4 sin(0) conic.

A: Sketch the graph of the conic r=185+4sin θ using a graphing calculator as shown below.

Q: A conic is given by r = 2 – cos 0 (a) Find the eccentricity and identify the conic. (b) Find the…

A: Compare with standard equation in polar then find e and using conditions of e determine the conic

Q: Graphing a Polar Equation (Limaçon without an Inner Loop) Graph the equation: r = 3 + 2 cosθ

A: We graph the given equation as,

Q: Graphing a Polar Equation (Limaçon with an Inner Loop) Graph the equation: r = 1 + 2 cos θ

A: The given polar equation is:r = 1 + 2 cos θ where r is the distance and θ is an angle. The graph of…

Q: Find a polar equation for each conic.For each,a focus is at the pole.e=1 directrix is parallel to…

A: Suppose d be the distance of the directrix, e be the eccentricity, then the polar equation for each…

Q: QUESTION 8 TM Given the polar equation r= 1+2 cos 0. i. Show that the graph of the equation is…

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Q: Exercise 2. Plot the graph of the function given in polar coordinates tanh 0-1 r = 2 Write analysis…

A: Given: r=2tanθθ-1since θ>1(radians)

Q: 4 1-2 sin 0 equation of the conic (b) Given r=- Find the distances from the pole to the vertices and…

A: The given curve is r=41-2sinθ. To find: Distances from the pole to the vertices, equation in…

Q: Homework: HW 9. 11 Identify the conic the polar equation and give the p 77+5cos 0 Is the directrix…

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Q: a) Circle c) Parabola d) Hyperbola 5. The Cartesian equation (x + 10)² + y² = 0 in polar form. b)…

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Q: r=6/(2+sin(t))

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Q: 29-46 Sketch the curve with the given polar equation by first sketching the graph of r as a function…

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Q: The radiation from a transmitting antenna is not uniform in all directions. The intensity from a…

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Q: Find a polar equation for the conic section with one focus at the origin, along with the given…

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Q: Solve, a. If necessary, write the equation in one of the standard forms for a conic in polar…

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Q: Graphing polar curves Graph the following equation. Use a graphing utility to check your work and…

A: we have to graph the equation in polar coordinates system. r2 = 16 cos θ

Q: According to Kepler's first law, a comet should have an elliptic, parabolic, or hyperbolic orbit…

A: From the table, ϑ=0.86, r=2.92ϑ=1.41, r=2.31

Q: 14 Sketch a graph of r = Use the graph to write a Cartesian equation for the conic. 4+ 3 cos(0) '…

A: We sketch the graph using a graphing calculator

Q: Find the polar equation that represents the conic described. (assume that a focus is at the origin.)…

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Q: Find a polar equation for each conic.For each,a focus is at the pole. e = 2/ 3 ; directrix is…

A: Consider that the conics has focus at the pole, eccentrcity e=23 and directrix parallel to the polar…

Q: Help!  Picture below

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Q: 1. The eccentricities of conic sections with one focus at the origin and the directrix corresponding…

A: Given e=2  and r=-2sec(theta ) Now we have to find the polar equation as shown below

Q: Topic: (Conics, Parametric Equations, Polar Coordinates) Graph the polar equation and find the area…

A: Given  r = 2- 6cosθ

Q: 14 Sketch a graph of r = Use the graph to write a Cartesian equation for the conic. 3+ 4 cos(8)…

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Q: A curve called the folium of Descartes can be represented by the parametric equations 3t2 3t and y =…

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Q: a. Identify the conic section that polar equation r =8/(2 + 2 sin θ)represents.b. Describe the…

A: a. The given equation is r=82+2sinθ. Rewrite this as r=41+sinθ.

Q: a. If necessary, write the equation in one of the standard forms for a conic in polar coordinates.b.…

A: (a) part Consider the given polar equation r=23-2 cosθ Or the given polar equation also can be…

Q: a. Identify the conic section that polar equation r =6/(3 - 2 cos θ)represents.b. Describe the…

A: Consider the given equation:r=63−2cosθObserve the equation:r=ed1−ecosθWhere e = eccentricity and d =…

Q: A conic is given by 1 r = 1+2 cos 0 (a) Find the equation of the conic in rectangular coordinates.…

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Q: 1. Sketch the graph of point P with the (2.) a. 4 2. Find the polar coordinates that correspond to…

A: We have yo plot the point P(2,3π/4) on graph

Q: Find the polar equation that represents the conic described. (assume that a focus is at the origin.)…

A: To find the polar equation for the conic described

Q: a. Identify the conic section that polar equation r =12/(2 - 4 cos θ)represents.b. Describe the…

A: We have polar form of conic section r=122-4 cosθ   Standard equation of conic section in polar form…

Q: 2. (a) Graph the polar equation r = 8 cos 0. What type of curve is this? (b) Convert the equation to…

A: Given r=8cosθ

Q: Prove that the polar equation of a planet's elliptical orbit is (1 – e²)a e cos 0' where e is the…

A: Given: eccentricity of the ellipse is e. length of major axis is 2a. let the equation of ellipse…

Q: 22 Sketch a graph of r = Use the graph to write a Cartesian equation for the conic. 6 + 5 sin(0)

A: Given  r=226+5sinθ For a conic with focus at origin , directrix  y=±p, p is a positive real number…

Q: 4 -4 -5- Find the parametric equations for the graph shown above given that when t = 0 the point on…

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Q: 6. Given the conic section r = find the x and y intercept(s) and the focus(foci). 5+ sin(0)…

A: Given, the conic section r=65+sinθ, find the x and y-intercepts and focus.

Q: EXAMPLE 7 Conic sections in polar coordinates Find the vertices, foci, and directrices of the…

A: Q a Given that: r=82+3cosθ…

Q: 1- a cos 8 3. A family of curves has polar equations r = 1+a cose: Invesigate how the graph changes…

A: Rule is that the denominator of the equation cannot be zero. Substitute values of a and θ in the…

Q: b). We all use antennas at our homes and a fact lies that antennas transmit some form of radiation.…

A: This is a case of multiple unrelated question. You have posted 3 different questions, tow of which…