Identify the quadratic surface of the equation 6x? + 3y? + 222 + 24x – 6y – 12z + 39 = 0 Choose an option: O one-leaf hyperboloid ellipsoid O cylindrical surface O elliptical paraboloid O cone-shaped surface O two-leaf hyperboloid O hyperbolic paraboloid O spherical surface

Q: Nhat is the equation of the parabola containing the points (2, 2), (4,-8), and (-2, –14)? O y = - 4x…

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Q: Describe the yz-intercept of the sphere with the equation x2 + y2+z2 - 2x+ 10z +5 = 0

A: The given equation of sphere is: x2+y2+z2-2x+10z+5=0

Q: . Use the method of completing the square to write the following equation in standard form and…

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Q: Identify the surface with equation 9x2 – 4y?+ 16z2 – 144 = 0.

A: Given: The equation 9x2-4y2+16z2-144=0 To find: The name of type of surface with the given equation.

Q: Find the center and radius of the sphere x + y + z² +4x+6y-10z+2=0 and graph the sphere.

A: x2+y2+z2+4x+6y-10z+2=0 We need to find the center and radius of the given sphere and graph the…

Q: Identify the surfaces of the following equations by converting them into quations in the Cartesian…

A: To identify the quadratic surface of the equation: Given: The equation of the surface is r=z2-1.…

Q: Find the x-intercepts of the parabola given by the equation. (If an answer does not exist, enter…

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Q: Draw the hyperbola with the equation: 3x? – 2y² + 6x – 8y = 6.

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Q: Write the equation of the hyperbola 4x2 – 25y? + 8x + 250y – 721 = 0 in standard form (x – h)? (y –…

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Q: Sketch or describe the surfaces in R³ of the equation presented x² + y} – 2x = 0

A: The equation is x2+y2-2x=0

Q: Write the equation of the hyperbola 9x² - 36y2 - 18x144y - 459 = 0 in standard form (x - h)² (y -…

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Q: Find the quadratic surface and sketch the graph of r+y +- 4xyz = 1

A: The given equation is: x2+y2+z2-4xyz=1

Q: 18. Identify the surface that corresponds to the equation 100y^2 - 25x^2- 4z^2 = 1. show solution

A: It represents hyperboloid.

Q: Find the point on the parabola y* = 2x that is nearest the point (1, 4).

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Q: Find the x-intercepts of the parabola given by the equation. (If an answer does not exist, enter…

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Q: Find the length of major axis of the ellipse x^2+4y^2-2x-8y+1=0

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Q: What is the equation of the directrix of the parabola x2 + 2x+4y– 27=0? A y=8 B y=0 (© y= -2 D y=6

A: Solution ) x2 + 2x + 4y - 27 = 0 Add 1 and subtract 1 in equation  x2 + 2x +1  - 1  + 4y - 27 = 0…

Q: 5. Identify the focus of the parabola given by y = 8x². O (0,) O (-8,0) O (0,0) O (8)

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Q: Show, by completing the square, that the parabolay = ax2 + bx +c can be obtained from y = ax 2 by a…

A: The given equation of parabola is y=ax2+bx+c. Rewrite the above equation as follows.…

Q: Find the points on the ellipse  X^2 + 6y^2 + 3xy =40 With the greatest x coordinator

A: Let us assume thatfx,y=xandgx,y=x2+6y2+3xy-40The lagrange multiplier equations…

Q: the coordinates of vertex, focus, and ends of latus rectum of the parabola  Y2−8Y+6X+16=0

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Q: What is the equation of the parabola that opens to the right and with vertex at (4,-2) and a latus…

A: Prabola

Q: Complete the square to find the vertex of this parabola. x² – 12y – 6x + 5 = 0 3,-

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Q: Find the point on the parabola y = (x – 3)² – 5 that is closest to the point (0,0). |

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Q: Find the points of intersection between the parabolas y = 6 - x 2 and y = x 2 - 2. %3D

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Q: b) Determine the concavity, Y-Intercept, X- intercept of the quadratic equation And sketch the…

A: Clearly shows the turning poin of the quadratic equation is (10, -50)

Q: (b) Find the evolute of the parabola y? = 4ax.

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Q: What is the standard form of equation of a parabola with vertex at the origin and directrix x = 3? A…

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Q: Complete the square to find the center and radius: x^2+y^2+2x+4y-1=0

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Q: Find the coordinates of the points of intersection of the parabola y = x2 and y = x+3.

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Q: The equation x² + 14x + y² – 8y +z2 +10z = – 65 represents a sphere whose center is (-7,4, – 5) |

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Q: A surface in space is defined by the equation -4x? + 16y- 8z2 = 0. Which one of these is true? O The…

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Q: Find the point on the parabola (y = x2/2) that is closest to the point (-4,1)

A: Use distance formula to evaluate

Q: Express the general form to its standard form and locate the center, vertices, covertices and foci…

A: equation 4x2 - y2 - 32x - 4y + 24 = 0

Q: Solve for the directrix of the parabola y2 + 8x = 32

A: We have to solve for the directrix of the parabola y2 + 8x = 32.

Q: Find the point on the ellipse x2 + 3y + 2xy = 6 with the greatest x-coordinate. (Use decimal…

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Q: Draw the hyperbola with the equation: 3x? – 2y² + 6x – 8y = 6. %3D

A: Given: 3x2−2y2+6x−8y=6

Q: Find the point on the parabola y 2 =2x that is closest to the  point ( 1, 4)

A: Given: y2=2x let's point on parabola is t22,t now, if point1,4 is closest to t22,t2 then product of…

Q: Find the points of intersection of the parabola with equation 2x + y² + 4y – 2 = 0 and the line…

A: Here we find the intersecting point of parabola and the line.

Q: Identify and sketch the surface -25x^2 +4y^2-100z^2=100.

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Q: 2. Which of the equations below also represents the parabola y=-3x² 18x + 16? Oy=3(x+3)² +65…

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Q: 6) Use the process of completing the square to transform the General Form equation below into…

A: Given,  x2+y2−10x−16y+53=0Concept used:x2−2ax+a2=x−a2

Q: In which variable(s) should you complete the square to identify the surfacex = y2 + 2y + z2 - 4z +…

A: We have to determine which variable should we complete the square to identify the surface…

Q: Find the point on the parabola y=x2 closest to (6,3

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Q: Write the equation of the hyperbola 9x² – 4y? – 54x + 32y – 19 = 0 in standard form (x – h)? (y –…

A: Write the equation of the hyperbola  9x2 - 4y2 -54x +32 y  -19 =0 In the standard form  (x-h)2 /a2 -…

Q: Identify and sketch the graph of the quadratic surface 4x2-y2-z=1

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Q: Write the equation of the hyperbola 25z – 16y + 150z + 64y- 239 = 0 in standard form %3D (2 - h) (y-…

A: Equation of hyperbola 25x2+ 150x-16y2+64y-239= 0 25( x2+6x)-16(y2-4y)= 239…

Q: 2. Which equation represents a parabola with vertex (4,4) and directrix y = 2? Oy=2x² - 4x + 4…

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Q: Determine F'(-3i) if 522 – 4z + 3 F(a) = | - vhere C is the ellipse 16x² + 9y² = 144.

A: The given ellipse can be written as: x232+y242=1 Thus the ellipse encloses y=-3.