Find an equation of the surface consisting of all points P(x, y, z) that are twice as far from the plane z = -4 as from the point (0, 0, 4). Identify the surface. Equation: Type of surface: Choose one▼

Q: (a) Find and identify the traces of the quadric surface x2 + y2 - z2 = 36 given the plane.

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Q: Find an equation of the surface of revolution generated by revolving the plane curve about the…

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Q: Describe the surface whose equation is x2 + y? + z2 + 6x + 8y + 8z – -16 = 0. Surface description:…

A: Given:- x2+y2+z2 +6x+8y+8z--16=  To find:- Surface description

Q: Analyze the trace when the surface z = (1/2)x2 + (1/4) y2 is intersected by the indicated planes.…

A: Consider the value of y=4

Q: Describe the surface with equation x² + y? + z? + 8x + 4y + 2z – 4 = 0) The surface is a sphere with…

A: Topic:-  sphere equation

Q: Find an equation of the surface consisting of all points P(x, y, z) that are twice as far from the…

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Q: The set of all points equidistant from the point (0, – 3, 0) and the plane y = 3 are represented by…

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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: Find the traces of the given surface in the planes x=k,y=k,z=k. Identify the surface and sketch it.

A: The given surface is 4x=y2+z2 We have to identify the surfaces in the planes x = k,  y = k and z =…

Q: The set of all points equidistant from the point (0, 2, 0) and the plane y = −2, find an equation of…

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Q: Sketch the portion of the surface that lies in the first octant: x = y. 12 1.5 1 0.5 0.15 . 0. . 2.

A: The given plane is in first octant and the plane is given by:  x = y

Q: 5. Plot the surface of 6x2 – 2.r – y?z2 = 0, for -10 <r, y, z < 10 %3D | |

A: To plot the given surface.

Q: Find the traces of the given surface in the planes x=k,y=k, z=k. Identify the surface and sketch

A: Quadric Surface Hyperboloid of two sheet z2c2-x2a2-y2b2=1 In this two variables have negative…

Q: Find an equation for the surface of revolution formed by revolving the curve in the indicated…

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Q: Classify and sketch the surface 4x2 − 3y2 + 12z2 + 12 = 0.

A: Solution:Given surface4x2 - 3y2 + 12z2 + 12 = 0    — 1divide equation 1 with -12,⇒ x2-3 + y2u - z2 -…

Q: escribe and sketch the surface in R*represented by the equation x + y = 2.

A: Given that - Describe and sketch the surface in R³ represented by the equation x + y = 2.

Q: 1. Find an equation for the set of points whose distance from the plane z =8 is twice the distance…

A: SOLUTION-

Q: identify the surface. 2x²-32² +6²-42-3y +2=0 Present a sketch of the surface, well defined.

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Q: Find an equation of the surface of revolution generated by revolving the plane curve about the…

A: Given:    Surface y2=z3 : about the z-axis. Find:- (a)Draw the graph of surface (b)an equation of…

Q: Locate and classify the stationary points on the surface z = Ty"- 2xy 2x2- 3x, remembering that r, y…

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Q: Find an equation for the surface consisting of all points P for which the distance from P to the…

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Q: Find the area of the surface. The surface in the first octant cut from the cylinder y = (2/3)z^(3/2)…

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Q: Describe the shape of the surface: x? + y2 = 9. How would you describe the curve of the intersection…

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Q: Q5) Find the equation of the surface formed by rotating the following line about the x -axis. 1=…

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Q: 9a2 + 4y? + 36z? = 36 %3D

A: given surface 9x2+4y2+36z2=36 claim- to find the trace of given surface in planes x=k , y=k , z=k ,…

Q: Find an equation of the surface of revolution generated by revolving the plane curve about the…

A: Given equation: x2=4y    which has to be revolved about the y-axis.

Q: Find an equation for the surface consisting of all points that are equidistant from the point (0,-…

A: Point (0, -3,0) Y= 3

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 the traces of the given surface in the planes x=k,  y=k, z=k. Identify the surface and sketch…

A: The given surface is 4x=y2+z2. We have to identify the surfaces in the planes x = k,  y = k and z =…

Q: 2? = a? + 2y?

A: Consider the given surface z2=x2+2y2 The trace in the plane x=k are z2-2y2=k2 For k=0, z2-2y2=0⇒…

Q: Find an equation for the surface obtained by rotating the line z = 2x about the z-axis. + x²) b. z?…

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Q: (a)) The base point of the surface is (0,0,0) and its axis (of symmetry) is the line (x, y, z) = (0,…

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Q: Find an equation of the surface of revolution generated by revolving the plane curve about the…

A: It is required to find the equation of the revolution generated by revolving the given plane about…

Q: Identify and sketch the section of the surface at x = 0. 2y? - x + 2z = 32 %3D Type of the surface:…

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Q: Consider the equation 4x² - 3y² + 12z² = -12. Describe the traces of this surface on the xy-plane,…

A: The traces of a surface are the cross-sections created when the surface intersects a plane parallel…

Q: = V16 – x², -2<x<3, is rotated about the x-axis. Find the area of the resulting surface.

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Q: Find an equation for the surface of revolution formed by revolving the curve in the indicated…

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Q: Identify and sketch the surfaces in space, 3-D. x² +y² = a² a) b) z = 4– x² – y² x² + y? - z? = 0 |

A: a)  x²+y² = a²

Q: Find an equation for the surface consisting of all points that are equidistant from the point (-4,…

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Q: Build surfaces and determine their appearance (name)x2+2y2-2z=0

A: Consider the provided equation,

Q: Identify and sketch the section of the surface at x = 0. 1 Туре: 61 61 61 61 4. 4 4. 4- 2 -8 -6 -4 4…

A: Let's find.

Q: Classify the quadric surface. −49x2 + y2 + z2 = 49

A: Given query is to find the shape of the surface.

Q: Describe and sketch the surface y2 + z2 = 9

A: the given equation represents the cylinder where it forms the circle as the base on yz plane and is…

Q: Describe and sketch the surface y2 + z = 6

A: Graph: Given surface y2+z=6 Since one co-ordinate has power 2 and other co-ordinate has power 1. So…

Q: Find the traces of the given surface in the planes x = k, y = k, z = k. Identify the surface and…

A: Given - The surface z = x2 - y2 To find - The traces of the given surface in the planes x = k, y =…

Q: Try to visualize the set of all points (x, y, z)in a coordinate space that are equidistant from the…

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Q: Find an equation for the surface generated by revolving the curve about the y-axis. y = 2x , (z = 0)…

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Q: x² + 9y² – 2² = 9

A: The given equation is: x2+9y2-z2=9           (1)

Q: Identify and sketch the section of the surface at x = 0. 16 16 Type of the surface:

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Q: .. .. Find an equation for the surface of revolution formed by revolving the curve in the indicated…

A: Given equation of curve is z2 = 4y The radius of function about y axis is  z2 = 4yz = 4yz = 2yr(y) =…