Classify the quadric surface given by equation  and  determine its standard  form. x2 + y2 − z2 − 2x − 4y − 4z + 1 = 0

Q: State the type of the quadratic surface: x^2−(y/8)^2+z^2=1 1. Hyperboloid of two sheets 2.…

A: The given question can be solved as shown in step 2.

Q: z =x' +y° +1 Y L x' +y? -z? = 1 LY

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Q: State the type of the quadratic surface: (x/8)2+(y/3)2+z^2=1 1. Hyperboloid of two sheets 2.…

A: Given that the type of the quadratic surface is    (x/8)2+(y/3)2+z2 = 1

Q: 2. Given the quadratic surface S by the equation below, determine the type of surface. 2x? + 3y? +?…

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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 of revolution by revolving the plane curve 3y = √(9- [(x-1)] ^2)…

A: We need to find the equation of the surface. Please find step by step solution below:

Q: Find the area of the surface. The part of the sphere x2 + y2 + z² = 4z that lies inside the…

A: Given sphere is x2+y2+z2=4z that lies inside the paraboloid  z=x2+y2. We have to find the area f the…

Q: Find the center and radius of the sphere X² + y² + z² −2x−4y + 8z + 17 = 0

A: Given: Equation of a sphere is x2+y2+z2-2x-4y+8z+17=0. To find the center and radius of the sphere.…

Q: Identify the type of surface represented by the equation z2 x2 %3D 10 10 6. Parabolic cylinder…

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Q: Reduce the equation to one of the standard forms, classify the surface, and sketch it…

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Q: Identify the type of surface represented by the given equation. 를 - 2.2 2 8. O Parabolic cylinder…

A: The given equation is z22-x28=y2. As we know that the general equation of the parabolic cylinder is…

Q: find a parametrization of the surface. The paraboloid z = x2 + y2, z<=4 The paraboloid z = 9 - x2…

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Q: Identify the surface by completing the squares. A hyperboloid of one sheet. O An elliptic cone. O A…

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Q: state the type of the quadric surface and describe the trace obtained by intersecting with the given…

A: Given: x2+y42+z2=1  ……1   Equation of plane is: z=14  ……2

Q: Find an equation of the surface of revolution by revolving the plane curve 3y = √(9- [(x-1)] ^2)…

A: We need to identify the quadratic surface.

Q: Consider the equation below. x² – y2 + z² – 4x – 2y – 4z + 7 = 0 - Reduce the equation to one of the…

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Q: Consider the surface z = (x+ 1)² + (y – 2)² – 1 - Select a correct name for this surface and point…

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Q: Classify the quadric surface. x2 - y2 + z = 0 O hyperboloid of one sheet O hyperboloid of two sheets…

A: Classify the quadratic surface.

Q: Find the center C and the radius a for the sphere 1. 3x2 + 3y2 + 3z2 + 2y - 2z = 9 2. x2 + y2 + z2 -…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: state the type of the quadric surface and describe the trace obtained by intersecting with the given…

A: x2+y42+ z2=1,y=5x2+y42+ z2=1

Q: A 2-D surface was found in one research group of scientists and a surface equation has been derived…

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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: cribe the surface with equation x + y° + z? + 8x + 4y + 2z – 43 = 0 surface is a sphere with center…

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Q: Find an equation for the sphere with center at (-7,8,0) and radius = 9 O x2 + y? O x2 + y2 + z- -…

A: We have to find

Q: b. z= 4x2 + 4y²

A: The equation describes surface of elliptic paroboloid.

Q: Write the equation of the sphere in standard form. x2 + y2 + z2 + 8x - 4y + 4z + 15 = 0 Find its…

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Q: Consider the equation 4x2 – 36y2 – 9z² – 8x – 144y + 18z = 149. (i) Transform the equation into one…

A: Given equation is 4x2-36x2-9z2-8x-144y+18z=149

Q: The surface whose equation is given by -x2 + y? + z2 – 1 = 0 is called a. an elliptic cone b. a…

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Q: Use  inertia  to  classify  the  quadric surface  given by equation. y2 − z2 − 9x − 4y + 8z − 12 = 0

A: We wish to use inertia to classify the quadric surface given by the following equation:  ------(1)…

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

A: The given data is: To identify the surfaces: z2=4+4r2

Q: state the type of the quadric surface and describe the trace obtained by intersecting with the given…

A: The given quadratic surface is  x2+y42+z2=1 , y=0

Q: I just need #36.

A: Given the equation

Q: Determine the projection of the surface - y² = z on the xy-plane? (H - Ellipse Нуperbola Two…

A: To determine the projection, z = 0 x2/3 -y2 = 0

Q: Find the equation of the sphere with center c= (0, -1, 2) and radius r= 5. O x2 + y + 1)2 + (z + 2)2…

A: Biref answer is given below.

Q: x² A quadric surface is defined by the equation: + 3y² = 3 + z 3 1. Solve the equation of the traces…

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Q: Find the equation of spheres passing through the circle x+y+z'-6x-2z+5 =0, y = 0 and touching the…

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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. z? -y? -x?+ 4x= 5 by-3 = x?+z² 2

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Q: Classify and sketch the surface 12x? – 3y? + 4z? = 12 What are the 3 traces? Show equations of the…

A: A quadratic surface is a hypersurface. It is nothing but the generalization of a conic section in…

Q: Consider the equation below. x2 - y2 + z2 - 4x - 2y – 2z + 4 = 0 Reduce the equation to one of the…

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Q: The part of the sphere x^2+y^2+z^2=4z that lies inside the paraboloid z=x^2+y^2

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Q: Find the area of the surface. 12. The part of the sphere x2 + y2 + z2 = 4z that lies inside the…

A: Solution:GivenSphere:   x2+y2+z2=4zParaboloid: z=x2+y2To find the area of the…

Q: Find the traces for the given surface: 16x? +16y² – 9z = 0. Then sketch and identify the surface.…

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Q: Identify the surfaces of equations in the Cartesian form. Show your complete solutions. (a) 2² = 4 +…

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Q: State the type of the quadratic surface: ()' + ()° + z : 1 1. Hyperboloid of two sheets 2.…

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Q: Identify the surface y-3=x²+z² paraboloid cylinder cone hyperboloid

A: y-3=x²+z²

Q: Describe and sketch the surface y2 + z2 = 16

A: Given equation is y2+z2=16

Q: (3) Consider the quadric surface S C R, having equation a2 + y? - z2 = 9. Find all lines through P…

A: General equation of line from point 3,-3,3 is x,y,z=3,-3,3+tl,m,n.  Substitute it in the quadratic…

Q: Identify the surface by completing the squares. x +16y² – z? – 14x + 32y + 8z = 0 O A hyperboloid of…

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Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.