Find a polar equation for the hyperbola with focus at the origin, directrix x = −2, and eccentricity e = 1.2.

Q: Find a polar equation for the conic Parabola with its focus at the pole and the vertex (2, π/2)

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

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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: find and sketch The polar equation for conic section with eccentricity(e=1) and with one of the…

A: See the explanation below

Q: Eliminate the parameter and obtain the standard form of the rectangular equation. Hyperbola: x = h +…

A: Hyperbola: x = h + a sec θ, y = k + b tan θ We need to eliminate the parameter to obtain the…

Q: 42. Hyperbola: = h+a sec 0, y= k+b tan 0

A: Use trigonometric function: 1+tan^2(theta) = sec^2(theta)

Q: Find the polar equation of the conic with focus at the origin and the given eccentricity and…

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Q: Find the eccentricity and the distance from the pole to the directrix of the conic. Then identify…

A: The standard form of the polar equation for a conic is  r=ep1±ecosθ Where e>0 is the eccentricity…

Q: а) Given a pair of parametric equations x =1-2t, y =r +4. i. Eliminate the parameter of t to obtain…

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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: 12. Find a polar equation for the hyperbola with focus at the origin, directrix x = -2, and…

A: Given- The hyperbola with focus at origin, directrix x=-2and eccentricity e=65. To Find- The…

Q: Write a polar equation for a conic having focus at the origin, directrix y = - 2, and eccentricity e…

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Q: Identify the conic section that the polar equation represents. Describe the location of a directrix…

A: Given the polar equation

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: 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: Find the polar equation for a parabola with its focus at the origin and whose directrix is y = -a…

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Q: Show that a conic with focus at the origin, eccentricity ,and directrix y=-d  has polar equation r…

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Q: The ellipse + 1 can be drawn with parametric equations where (t) is written in the form 4²2 r(t) = r…

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Q: Identify the conic with a focus at the origin, and then give the directrix and eccentricity. (Use…

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Q: Write a polar equation of a conic with the focus at the origin and the given data. hyperbola,…

A: Given: Focus (0, 0) Eccentricity = e =2.5 Directrix = d = 2 The formula for polar equation of any…

Q: Q3 : Find and sketch the polar equation for conic section with eccentricity (e = 1) and with one of…

A: Please see the explanation below.

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

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Q: Find the polar equation of the conic with focus at the origin and the given eccentricity and…

A: Topic-polar equation

Q: r = 2– sin(0)"

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Q: Find the polar equation of the conic with focus at the origin and the given eccentricity and…

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Q: give the eccentricities of conic sections with one focus at the origin along with the directrix…

A: Given: The eccentricities of conic sections with one focus at the origin along with the directrix…

Q: Find a polar equation for a parabola that has its focus at the originand whose directrix is the line…

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Q: 2 Find a polar equation of the hyperbola (5)' – ()² = 1. p2 Note: use t for 0.

A: To find the polar form of hyperbola equation

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

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Q: Find a polar equation for the conic Ellipse with its focus at the pole and the eccentricity e = 3/4…

A: Focus of the ellipse is at the pole. Eccentricity is e=34. Directrix is y=-2. Comparing the…

Q: The ellipse 32 = 1 can be drawn with parametric equations where x(t) is written in the form 72 x(t)…

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Q: Eliminate the parameter and obtain the standard form of the rectangular equation. Ellipse: x = h + a…

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Q: Determine the polar equation of a hyperbola with the eccentricity of 3 and directrix y =2

A: Polar equation of hyperbola, when directrix is the line y=d is , where e is for eccentricity and d…

Q: Find a polar equation for the conic Hyperbola with its focus at the pole and the given eccentricity…

A: To find a polar equation for the conic Hyperbola with its focus at the pole and the given…

Q: Write a polar equation of a conic with the focus at the origin and the given data. ellipse,…

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Q: Find the eccentricity e and the distance |d| from the pole to the directrix of the coni -6 r = 3 + 5…

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Q: Write a polar equation of a conic with the focus at the origin and the given data.  parabola,…

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Q: Find a Cartesian equation for the hyperbola centered at the origin that has a focus at (3, 0) and…

A: The focus is 3,0 c,0=3,0∴c=3 Also the directrix x=ae=1                           ∴a=e Now…

Q: Find a polar equation in the form r = f(8) of the hyperbola with eccentricity e = 4 such that one of…

A: One of the foci            =0,0    poleeccentricity                   = 4vertex nearest to pole =…

Q: Write a polar equation of a conic with the focus at the origin and the given data. hyperbola,…

A: The given data of the hyperbola with focus at the origin is

Q: parabola, directrix x- -7

A: r=ed1-ecosθd is the directrix

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

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Q: Find a polar equation for the ellipse with the following characteristics. Focus: (0, 0)…

A: To find A polar equation for the ellipse with the following characteristics. Focus: (0, 0)…

Q: Find the polar equation of the conic with focus at the origin and the given eccentricity and…

A: We know eccentricity is the Ratio of distance between variable point to directrix to distance…

Q: Find and sketch the polar equation for conic section with eccentricity (e = 1) and with one of the…

A: Equation of conic with eccentricity e=1 is a parabola  focus =(0,0) directrix y=-1 (0.-1) vertex…

Q: Write a polar equation of a conic with the focus at the origin and the given data. ellipse,…

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Q: Find a polar equation for the conic Hyperbola with its focus at the pole and the eccentricity e =…

A: We have:  eccentricity e = 52 directrix x = -1 distance between the focus (pole) and the directrix =…

Q: Identify the conic with a focus at the origin, and then give the directrix and eccentricity. (Use…

A: r=93+2cosθ  Rearranging this, we get  r=931+23cosθ    r=31+23cosθ