Classify the quadric surface. 9x2 + 3y2 − 6z2 = 54

Q: Show that the equation represents a sphere, and find its center and radius: 2x2+2y2+2z2=8x-24z+1

A: To show that the equation represents a sphere, and find its center and radius: 2x2+2y2+2z2=8x-24z+1

Q: determine the type of the quadric surface. ) + G)° + 2:² = 1

A: To determine the type of quadric surface(x3)2+(y4)2+2z2=1

Q: Find the equation in rectangular coordinates of the quadric surfaceconsisting of the two cones φ =…

A: The relation between spherical and rectangular coordinates in polar form is given by the following…

Q: (a) Identify and graph the quadric surface -r - y + 2? = 1.

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Q: Find the equation of sphere having its centre on the line 2x - 3y = 0 = 5y + 2z and passing through…

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Q: Find the center and the radius of the sphere x + y² += - 4x+ y-6z+13=0 Center: Radius:

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Q: Build a surface and determine their appearance (name).-4x2+12y2-3z2+24=0

A: Find the surfaces for x = 0, y= 0 and z = 0.

Q: Find the point on the sphere x2+y2+z2=1089 that is farthest from the point (-22,-17,-21).

A: Let, (x,y,z) be the point on the sphere g(x,y,z)=x2+y2+z2-1089=0...(1) which the maximum distance…

Q: Write the sphere in standard form. 4x2 + 4y2 + 4z2 − 32x + 16y = 1

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Q: Identify the quadratic surface, explain the shape and describe the traces. 1. a) x^2 + y^2 + 1/2…

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Q: x² y? + z = 1 4 9.

A: Given equation  x^2/9 - y^2/4 +z = 1 this is equation of hyperbolic Paraboloid.  Quadratic Surface…

Q: a) Find the distance between the points (7,0,1) and (-5,4,2). b) Find the center and radius of the…

A: According to our guidelines we can answer only three subparts ,or first question and rest can be…

Q: 1. (a.) Name the given quadric surface and give its axis (c.) Name its trace on y = 2. 45x² + 20y +…

A: Given : An equation 45x2+20y2+36z=0 To find: a) Name of given quadratic surface              b)…

Q: Identify the type of surface (in space) given by the equation, and sketch the surface. a. x^2+y^2=25

A: Note: - Since you have asked multiple questions, we will solve the first question for you. If you…

Q: Find the center and radius of the spherex2+y2+z2−6x−16y+ 20z=−92.

A: Topic - center and radius of sphere

Q: Identify and sketch the quadric -- = 0 3 2 3 surface z 2

A: For the solution of the problem follow the next step.

Q: a) [. Show that the equation 6x + 6y6z + 3x² + 3y² + 3z² = 18 represents a sphere, and find its…

A: Note: Hi! Thank you for the question as per the honor code, we’ll answer the first question since…

Q: Find the center and the radius of the sphere. x2+y2+z2-3x-6z=0

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Q: Identify and choose the appropriate quadric surface. 36z = x + 6v

A: First try for different values of x,y,z and see where the graph lies.

Q: Find the center and the radius of the sphere. x2+y2+z2+3x+3z=

A: See the details solution in below

Q: Describe the shape formed by the intersection of the plane and the solid. 1. 2. 3.

A: Cut the given solid and visualise the cross sectional area that is the intersection of plane and…

Q: 9. Write the equation of the quadric surface in standard form then identify the quadric surface…

A: The standard form of quadric surface : Ax2+By2+Cz2+Dxy+Exz+Fyz+Gx+Hy+Iz+J=0…

Q: Show that the equation represents a sphere, and find its center and radius: x^2+y^2+ z^2-8x + 6y +…

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Q: 6x2 - 4xy + 6y2 + 16z2 - 33 = O 6 -2 -2 A = 16 Find the equation of the rotated quadratic surface in…

A: For the equation ax2+by2+cz2+2f yz+2g zx++2hxy, the matrix is ahghbfgfc

Q: c) [. The intersection of the sphere B and the xz-plane is (x - 2)² + (z + 1)² 2)² + (z + 1)² = 9.…

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Q: determine the type of the quadric surface (x/3)2+(y/4)2+ 2z2 = 1

A: Here we have to determine the type of quadric surface.  x32+y42+2z2=1

Q: Find an equation for the sphere with a) center at the origin and radius length r = b) center (2, –…

A: Let the coordinates of centre of sphere be a, b, c and radius be r.

Q: Which quadric surface is this? *- ² + = 1 | Hyperboloid of One Sheet Hvnorholeid of Two Shoots

A: We are asked to identify the quadratic surface,

Q: Plot the surfaces over the indicated domains. Ifyou can, rotate the surface into different viewing…

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Q: Find the distance the point P(2,0,1) is form the plane 3x – 6y + 2z = 15. -

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Q: Find an equation of the largest sphere contained in the cube determined by the planes x = 0, x = 8,…

A: given the planes:

Q: Find an equation of the sphere concentric with the sphere x^2 + y^2 + z^2 + 4x + 2y − 6z + 10 = 0…

A: Topic = Geometry

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: The length of the major axis of the cllipse with center (-4, 1), minor axis parallel to the y-axis…

A: Equation of ellipse with center (-4,1) is given by

Q: Write the equation for a sphere centered at the point ( – 1, 7, 6) and the point ( – 7, 7, – 5) is…

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Q: Determine the center and radius of the sphere 2x2+2y2+2z2-12x-24y-36z=0

A: We have to find center and radius

Q: 4x² + 4y2 +422-8x + 16y=1 presents a sphere, and find its center and radius.

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Q: Simplify and identify the quadric surface, given: 9x2 – 18x + 4y² + 16y – 36z + 25 = 0

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Q: Find the equation of the xy-trace of the sphere. (x + 2)2 + (y + 1)2 + (z − 3)2 = 25

A: The equation of the sphere: - The general equation of a sphere is (x – a)2+(y-b)2+(z-c)2=r2 if (a,…

Q: Determine the equation for the sphere whose center and radius are given. Center Radius V13 (1,3,1)

A: Let center h,k,l=1,3,1 and radius r. Equation of the sphere with center h,k,l and radius r is given…

Q: The surface 2x2 -2y² – 2z² =1 is identified as

A: The given surface is qudratic surface. Different qudratic surfaces 1)Ellipsoid 2)Hyperboloid in one…

Q: Find the center and radius of the sphere x2 + 18x + y? + 4y + z2 + 10z = –74 Center: ( || ) Radius:

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Q: Identify and choose the appropriate quadric surface. 121z – 36y – 121x = 43

A: Given, 121z²-36y²-121x²=4356---------equation 1

Q: Identify and sketch manually the graph of the quadric surface 25x² -25y² -9z²-150x + 200 = 0.

A: Solution :-

Q: Rewrite the given equation of a quadratic surface and identify the graph. 12y2 – 3z2 = 16x

A: equation of the hyperbolic paraboloid  A y2 - B z2 = 2 Cx

Q: Identify the surface generated by the equation 9y^2 + 4x^2 - z^2 = 36 hyperboloid of 1 sheet,…

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Q: Identify and sketch by hand the graph of the quadric surface 25r2 – 25y? – 9z2 – 150r + 200 = 0. You…

A: An equation is given                              25x2-25y2-9z2-150x+200=0We have to identigy and…

Q: find the equation of a sphere. x^2 +y^2 + z^2 +2x - 2z -2 = 0

A: see the details solution in below

Q: Find an equation of the sphere with center (-4, 2, 8) and radius What is the intersection of this…

A: Given centre -4,2,8 and radius 5 of the sphere .The equation of a sphere is given by the…

Q: The equation of a surface, with respect to an orthonormal coordinate system for three-dimensional…

A: Every surface equation with respect to an orthonormal coordinate system is written in a matrix form…