Name the conic that has the given properties and find its Cartesian equation. Eccentricity 5/3 and vertices (0, ±3

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

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Q: hyperbola, vertices (±3, 0), foci (±6, 0)

A: Equation of hyperbola :x2a2 - y2b2 =1 , when vertices is on the x-axis.

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: Find an equation for the conic that satisfies the given conditions ellipse, foci (0, +9), vertices…

A: Solve the following

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

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Q: Find an equation for the conic that satisfies the given conditions. parabola, focus (5, -3), vertex…

A: The general form of the parabola is given by: y=a(x-h)2+k...(1) where (h,k( is the vertex of the…

Q: find the eccentricity, identify the conic, give an equation of the directrix and sketch the graph of…

A: Solution is given below:

Q: Identify the type of conic, assuming a > 0: r = 1+ V7sine Ellipse. O Parabola. O Hyperbola.

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Q: The conic with eccentricity e = 1/2 is a a) circle c) ellipse b) parabola d) hyperbola

A: step:-1 Eccentricity (e) :- The eccentricity e of a conic section is defined to be the ratio of the…

Q: Write a polar equation of a conic that has its focus at the origin and satisfies the given…

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Q: Write a polar equation of the conic that is named and described as, Hyperbola: a focus at the pole;…

A: Given information: Focus of hyperbola is at pole. directrix: x=-1 , which is vertical directrix.…

Q: Given the following conic section, determine its shape and then sketch its graph. 52? + 4y? + 3х +…

A: Since the coefficient of x2 and y2 are different and they both have positive signs, so it is an…

Q: Which conic section is formed in the image shown? O Circle O Parabola Ellipse O Hyperbola

A: we have to select the formation of an image

Q: Convert the following equation to standard form. Find the center, foci, vertices, asymptotes and the…

A: Given :

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

A: Given that: The eccentricity (e) = 6 Directrix (r) = -5 csc(theta) r=-5cscθr=-5sinθrsinθ=-5…

Q: 3. Write the equation of the following conic section in standard form and sketch the graph. Make…

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Q: Given the following conic section, determine its shape and then sketch its graph. 5x? + 4y? + 3x +…

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Q: Given the following conic section, determine its shape and then sketch its graph. a? – 2ry + y² + x…

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Q: Find the center, foci, vertices, asymptotes, and radius, as appropriate, of the conic section......…

A: Given, x2 + 2x + 4y - 3 = 0

Q: Find the standard form of the equation of the conic section satisfying the given conditions,…

A: Given focus is (-2,6) and the directrix is x=8.

Q: Find an equation for the conic that satisfies the given conditions. parabola, focus (2, -4), vertex…

A: The focus and vertex lie on a line x=2 and the focus is below the vertex. Hence this is a downward…

Q: Identify the conic section defined by the following equation. Sketch its graph. Label its vertices,…

A: Given 16x2-9y2+96x+54y-81=0

Q: ellipse, eccentricity 0.4, vertex (1, 7/2)

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Q: Given the following conic section, determine its shape and then sketch its graph. a – 2xy + y² +x –…

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Q: this conic is rotated counter-clockwise about the origin through an angle 37/4, rite the resulting…

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Q: Find the focus equation of the directrices, length of major axis, minor axis and focal diameters and…

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Q: identify the type of conic, the eccentricity, and the equation of the directrix.  r = 12/4 + 3 cos θ

A: To find: The type of conic, the eccentricity, and the equation of the directrix. Given information:…

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

A: Given: r = 84 + cos θ To identify: The type of conic, the eccentricity, and the equation of the…

Q: 2. Identify the conic as a hyperbola, parabola, or ellipse and find the foci (c) 4x = y? %3D

A: identify the conic and use the equation to find the focus,

Q: Name the conic that has the given properties and find its Cartesian equation. Eccentricity 1,…

A: A conic section is obtained by slicing the cones at different angles. There are three types of…

Q: Name the conic that has the given properties and find its Cartesian equation. Vertices (±2, 0) and…

A: The standard form of the hyperbola with center at origin is .  Here, are the vertices and…

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

A: An ellipse, eccentricity is 0.5 and vertex is at 1,π2.

Q: If a conic has rmin = 9 and rmax = 17 , find the eccentricity and semi-major axis.

A: Answer is mentioned below

Q: Find an equation for the conic that satisfies the given conditions. Ellipse, foci (±3, 0), vertices…

A: Solved below

Q: Solve for the equation in standard form of the following conic sections and graph the curve on a…

A: An equation of the ellipse is of the form, x2a2+y2b2=1 Equation of the ellipse through the point…

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

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Q: Identify the type of conic section whose equation is given and find the vertices and foci. y? – 2 =…

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Q: ) Find a trig. identity that will help you eliminate t. This will be one-half of a familiar conic,…

A: In the given equation, the concept of a trigonometric function is applied. Trigonometric Functions…

Q: If a conic has rmin = 18 and rmax = 30, find the eccentricity and semi-major axis

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Q: Identify this conic, list the necessary parts and then graph it: 2x2 +2y2 +8x=7

A: Given the equation of conic

Q: The eccentricity of the conic section below is 1 Enter

A: The given conic section is a parabola. Which is of the form  (x-h)2 =4ay

Q: Find the focus, equation of the directrices, lengths of major axis, minor axis and focal diameters,…

A: Please see the explanation below

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

A: let d be positive, a directrix x = d, and focus is at the origin.

Q: Identify what type of conic section is given by the equation below and then find the center, foci,…

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Q: Identify what type of conic section is given by the equation below and then find the center, foci,…

A: the given equation of the curve is: 4x2-24x-4y+28=y2 we have to identify what type of conic section…

Q: 3. x2 – 8x + y² + 6y = 0

A: To identify the conic section from the given equation.

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

A:

Q: 11. X-3x+5y-930

A: We find find what this equation represents as following.

Q: Name the conic that has the given properties and find its Cartesian equation. Vertices (±4, 0) and…

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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