Name the conic that has the given properties and find its Cartesian equation. Vertices (±4, 0) and eccentricity 1/2 .

Q: Find an equation for the conic that sa tisfies the given conditions. parabola, focus (-4, 0),…

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

A: Note:  For a Conic with eccentricity e,         i) if 0≤e<1, then the conic is an ellipse.…

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

A: e=1/2, x=1

Q: Determine what type of conic section corresponds to the given equation. 2x(x + 5) – y = 1 + y? O…

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

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Q: Rotate the coordinate axes to remove the xy-term. Then name the conic section and sketch its graph.…

A: Given: x2+4xy-2y2-6=0 To Find: Rotate the coordinate axes to remove the xy-term.Then name the conic…

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

A: Given :

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

A: e=32 , x=-4

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

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Q: Identify the conic section given by the following equation. x² + y² = 78x – 84y – 3116 - Select the…

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

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Q: What conic section is described by the following equation? 4.x2 + y? + 8x + 4y = 15 O Parabola O…

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

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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: Find a polar equation for the conic Parabola with its focus at the pole and the eccentricity e = 1…

A: Focus is at pole and the eccentricity e=1 and directrix x=5. The equation of the parabola with…

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. x² – 2ry + y² + x…

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

A: The eccentricity of a conic section is a deviation of the curve from the circularity. In simple…

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: Find a polar equation of the indicated conic in terms of r with the given characteristics and focus…

A: To find - Find a polar equation of the indicated conic in terms of r with the given characteristics…

Q: Find the equation of the conic with focus at the origin, eccentricity e and the directrix y = d.

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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: identify the type of conic, the eccentricity, and the equation of the directrix. r = 8/4 + 3 cos θ

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Q: 9. r = 6+2 cos 0

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

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Q: Eliminate the parameter, An ellipse: x = h + a cos t, y = k + b sin t. Write the resulting equation…

A: Let's consider the given equations for the ellipse:…

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

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

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

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

A: 1)Given,e = 1, y = 2 Equation of conic with eccentricity e and directrix y=k corresponding to focus…

Q: parabola, directrix x- -7

A: r=ed1-ecosθd is the directrix

Q: Identify the conic section as a parabola, ellipse, circle, or hyperbola, or if there is not enough…

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Q: Identify the conic section as a parabola, ellipse, circle, or hyperbola, or if there is not enough…

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Q: Find an equation for the conic that satisfies the given conditions.Parabola, focus(3,6) ,…

A: *to find:- equation of conic. *given:- focus, F(3,6) vertex, V(3,2)

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

A: e=1  &  y=2 Now directrix is, y=p⇒p=2

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

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

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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