In this exercise, traces of the surfaces in the planes are conic sections. In cach part, find an equation of the trace, and state whether it is an ellipse, a circle, a parabola, or a hyperbola. (a) 70? + y? + z? =7, y = 1. Equation: Choose one 1 (b) 36x? + - z? = 36, 2 =

Q: In this exercise, traces of the surfaces in the planes are conic sections. In each part, find an…

A: As this is a multiple subpart question according to the Bartleby Answering rule, only first three…

Q: 4. The upper half of the ellipse centered at the origin with axes of length 2a and 2b is described…

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Q: What is the equation of the parabola with vertex at (0, 0) and directrix y = -8 in standard form?…

A: Given that, vertex of parabola is (h, k) = (0, 0) diretrix of parabola is, y = -8 We have to find…

Q: Do I have to use the equations for the asymptotes of a hyperbola centered at the origin, y = tr or y…

A: The equations for the asymptotes of a hyperbola centered at the origin is y = ±bax or y = ± abx.…

Q: What is the standard form of the parabola, y + 2x + 10y + 9 = 0, given in conic form?

A: Do some rearrangement in the equation of given conic to convert it in standard form of equation

Q: What is the general equation of a parabola that opens upward with V(-1,2)?What is the equation of a…

A: Consider the given vertex. V=(-1,2)

Q: Find a parametrisation of the hyperbola that is obtained by translating the hyperbola with equation…

A: Here we need to find the effect of translation on parametric equation of hyprabola.

Q: What is the standard form of the equation of the parabola with the focus (5, –1) and the directrix æ…

A: Any point at parabola is equidistant from its focus and directrix.

Q: Find an equation of the hyperbola that has foci at (-13,0) and (13,0), and asymptotes y=3/2x and…

A: Given:

Q: Find the equation of the conic section indicated. Parabola with focus (8, 0), directrix x = −8

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Q: Find an equation of the hyperbola that has foci at (0,-13) and (0,13), and asymptotes y=5/12x and…

A: The hyperbola that has foci at (0,-13) and (0,13), and asymptotes y=5/12x and y=-5/12x. To find…

Q: Which is the standard equation of the hyperbola centered at the origin, with a vertical transverse…

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Q: Given a parabola's focus at (6, −4) and directrix at y = −7, how would you write its equation?

A: Equation of parabola: x-h2=4py-k Where vertex is (h, k) Focus is (h, k+p) And directrix y = k - p

Q: Sketch the hyperbola 9x² – 4y² – 18x + 8y – 31 = 0, and label the center, foci and vertices. Find…

A: Given : 9x2-4y2-18x+8y-31=0

Q: Find the largest and smallest distances from the origin to the conic whose equation is 5x2 − 6xy +…

A: To find the largest and smallest distances from the origin to the conic whose equation is 5x2 − 6xy…

Q: Determine the DE for: Parabolas with axis to the x- axis and with distance from focus to  vertex…

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Q: 2 Write the equation of the hyperbola – 25 · x? + 16 · y² = 400 in standard form + = 1 %3D

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Q: Identify the conic, analyze the equation (center, radius, vertices, foci, eccentricity, directrix,…

A: Consider the given second-degree equation: x2+10x-12y+13=0 Here, the objective is to identify the…

Q: Find the center, foci, vertices, and eccentricity of the hyperbola                         ( y +…

A: y+32225-x-5264=1⇒y--32152-x-5282=1 Now comparing with y-k2a2-x-h2b2=1, we get k=-3, h=5, a=15 &…

Q: The parabola y2 =-14x has it's focus at the point (b,0) where b is?

A: The standard equation of parabola for this condition is y2=-4ax here  Focus (-a, 0)   Now, we have…

Q: A cooling tower for a nuclear reactor is to be constructed in the shape of a hyperboloid of one…

A: Given a cooling tower for a nuclear reactor is to be constructed in the shape of a hyperboloid of…

Q: what is the equation of a parabola with a vertex at (4, 8) and a directrix at y=5

A:

Q: Find an equation of the hyperbola that has foci at (-2, 0) and (2, 0), and asymptotes y = x and…

A: The hyperbola has foci at -2,0 and 2,0 and asymptotes y=x and y=-x

Q: 2. Which conic section is represented by the équation 2x2 + 4x- y +9 = 0? O Hyperbola Ellipse O…

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Q: Find an equation of the hyperbola that has foci at (0, -10) and (0, 10), and asymptotes y = 1 x and…

A: To find the equation of hyperbola

Q: Which is the equation of a hyperbola with directrices at x = ±2 and foci at (4, 0) and (−4, 0)?

A:

Q: What is the equation of the standard hyperbola with vertices at (0, t a) and foci at (0, ± c)?…

A: Option B is correct.

Q: Show that the ellipse x*/a? + y*/b? = 1 and the hyperbola x/A? – y/B² = 1 are orthogonal…

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Q: Find the standard form of the equation of the hyperbola satisfying the given conditions as End point…

A: Find the standard form of the equation of the hyperbola satisfying the given conditions as End point…

Q: 4. Classify the following conics as a circle, parabola, ellipse or hyperbola and explain why. a) 9x?…

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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: A landscape architect is designing an elliptical pool that will fit in the center of a 20-by-30-…

A:

Q: 5. Which conic section is represented by the equation 36x² + 8y = 81? %3D Hyperbola Circle Ellipse…

A:

Q: Find the equation in xy coordinates for the conic section that satisfies the following conditions:…

A:

Q: Find the equation of the surface of revolution generated by rotating the hyperbola x^2 - y ^2=1 ,…

A: \ Revolution of the hyperbola about its transverse axis generates a surface of two sheets, two…

Q: What is the equation of the parabola with a vertex at (4.8) and a directrix at y = 53

A: This is a simple question based on conic section (Topic is parabola) before attempting this question…

Q: How is the distance between vertices for hyperbola equal to 2a?

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Q: DId entify, and find the goneraLequabion of the ellipse that ghares avertex and focus with the para…

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Q: Sketch the conic sections. Indicate the foci, and show your work: A) 4x2+3y2+8x-6y=5 B)…

A: A)Given equation is,

Q: What is the equation of the directrix of a parabola having vertex at (4, 3) and focus which is 2…

A:

Q: One of St. Matthew's Hall is 10 feet wide and has a semi- ellipse ceiling. The ceiling is 6 feet…

A:

Q: What is the equation of the parabola with vertex at (0, 0) and directrix y = 3 in standard form.…

A: Given vertex 0,0 and directrix y=3. We have to find equation of parabola.

Q: Which is the corresponding equation of the hyperbola with foci located at (−8, 0) and (8, 0) and a…

A: Given data is : Foci are -8,0 and 8,0 The transverse axis is 14 unit

Q: For the equation 9x + 4y - 54x-8y-59 = 0, classify the conic section, put the equation in standard…

A: Explanation: Given that,  9x2+4y2-54x-8y-59=0   Here we use the completing the square method in term…

Q: Find an equation of the hyperbola that has foci at (-10, 0) and (10, 0), and asymptotes y = 7x and…

A:

Q: Find the standard form equation for a hyperbola with vertices at (0, 21) and (U, y = 74 T

A: Given :Vertices : 0, 21 and 0, -21y=74x

Q: Deandre, an engineering intern was asked by his fellow students to heip them determine the standard…

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