The quadric surface x? – y2 - = 1 Find the xy – trace Find the yz-trace Find the xz-trace Do you see a trace parallel to one of the above traces? If yes, then what is that? Draw each trace separately on the two-dimensional plane.

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: 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: The top of a rubber bushing 1 surface of revolution generated by revolving the curve z= +1, (0sys2)…

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Q: (b) Sketch the trace of the surface z = 2x? – y? when x = -1. Label your axes, and give the…

A: Given surface is  z=2x2-y2          (i) By putting x=-1 in (i), the surface becomes z=2-y2 The graph…

Q: b) The curve y = }(r² – 2 In r), 1<r< 4, is rotated about the y-axis. Find the area of the resulting…

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Q: Let S be the quadric with equation 36x2 – 4y2 – 922 – 36x 0. - - (a) Classify the graph of S. (b)…

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Q: Consider the surface given by x²z+ 2yz2 = 3æy?. %3D (a) Find and (b) Find the tangent plane to the…

A: Surface given, x2z+2yz2=3xy2 ....(i) a)we have to find ∂z∂x  and ∂z∂y  Take equation (i) and…

Q: a). ii) Find the exact area of the surface obtained by rotating the curve 1 + 2 6x M about the…

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Q: Identify the quadric surface z =- y? -* as an ellipsoid, hyperboloid of one sheet, hyperboloid of…

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Q: Let B be the surface with equation x = -1+ /y. (a) Provide a hand-drawn sketch of B. Label the…

A: We are given that B as the surface with equation x=-1+y2. For (a), Let us sketch the surface B. It…

Q: Given the surface 9x^2 − 4z^2 = 9y. Find its traces on each coordinate plane and on the planes y=4,…

A: Solutions

Q: State the type of the quadratic surface: 2 ()° + (;)° + (;)° = 1 2 1. Ellipsoid 2. Hyperboloid of…

A: We know the general equation of ellipsoid with center at origin (h,k,l) is, We know the general…

Q: 2. Consider the two surfaces zx = x² + y? and z³ = 4(x² + y³) They have a curve of intersection C…

A: a) The two surfaces are zx=x2+y2 and z3=4x2+y2. To find the curve of intersection of these two…

Q: The surface S formed by the point P(x,y,z) such that the distance from P to the point A(1.0,-1) is…

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Q: 1. (a.) Name the given quadric surface and give its axis. (b.) Sketch the surface. (c.) Name its…

A: The given curve is -100x2+36y2+225z2=900. (a) To identify: The name of the given curve and its axis.…

Q: x2 Consider the surface T with equation 4 (y – 3)² + z2 = 1. 3 Find an equation of the trace of T on…

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

A: SOLUTION-

Q: Consider the surface defined by the equation 2.x2 – 2y2 – z = 0. (a) Choose any one of the variables…

A: The equation is the form z=f(x,y) represents a surface in the space. In this problem the equation of…

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

A: Givenx2-(y4)2+z2=1Since both variables are squared and have opposite signs the conic is a hyperbola…

Q: Identify and sketch the section of the surface at x = 0. 2y – x² + 2z? = 8 Type of the surface:…

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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: 4. Consider the surface defined by the portion of the cone z = -Vx2 + y? that lies below the…

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Q: Consider the surface S with equation (х — 2)2 + y?. 4 3 (a) Find an equation of the trace of S on…

A: We have to find the equation of the trace of S on the planes x=2, y=0, z=0 and z=3. We have to…

Q: The quadric surfaces y = z and 6z 3x + 2yʻ intersect as shown above. We can describe this…

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Q: Consider the surface in 3D described by the equation z = x² + y? – 16. (You might want to start by…

A: We are given that z=x2+y2-16 which is an Elliptical Paraboloid. We have to describe the trace in xy…

Q: 4. The surface described by the equation x2 + y + z² = 0 is a(an) (a) elliptic paraboloid symmetric…

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Q: Let S be the surface with equation (z - 4)² = 4x² + 4y². Viewing S as a surface of revolution, find…

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Q: 28.) What surface is the graph of (x-1) =y² +z? ? (a) A cone (b) A hyperbolic paraboloid (c) A…

A: The surface is a cone with vertex at (1,0,0).

Q: The surface defined by the equation z= 4x2 + y2 is called an elliptical paraboloid. a. Write the…

A: Given, function

Q: 32. Which of the following is the trace of the surface in the plane y=3? * O Hyperbola O Ellipse O…

A: Given, To evaluate trace of the surface in the plane at y=3

Q: Given surface A: 4x² − 9y² = 9(z² + 4) 1. Identify the type of quadric surface for A. 2. Give an…

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Q: Given: cylinder S in R^3 with equation x = z^2 + 2 (a) Sketch the graph of S in R^3. Indicate proper…

A: Given that x = z2 + 2

Q: 1 Let B be the surface with equation x = -1+ - y. 2 (a) Provide a hand-drawn sketch of B. Label the…

A: Given x=-1+12y

Q: The given curve is rotated about the y-axis. Find thearea of the resulting surface.   x =  1/4 x2 -…

A: If the curve y = f(x) , a≤x≤b is rotated about y axis , then surface area is, A=2π∫abx1+f'x2d

Q: る The quadric surfaces 3x y and 5z: = x² – y intersect in a curve. %3D %3D Parametrize this curve.…

A: To find the parametrized curve of the intersection curve we first find the intersection curve…

Q: Consider the surface z = 4x2 + y? + 1. An equation for the tangent plane to this surface at the…

A: Let fx,y=z. Differentiate the function f(x,y) partially with respect to x and y, to find fx and fy .…

Q: The surface x2+y?+z?-4x-2z+5=0 is: O an elliptic paraboloid O a point O no graph O a hyperboloid of…

A: Please see the below picture for detailed solution.

Q: Compute the surface area of the surface generated by revolving one arch of the cycloid…

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Q: 1. (a.) Name the given quadric surface and give its axis. (b.) Sketch the surface. (c.) Name its…

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Q: a) i) Find the exact length of the curve 1 + 4 15x3 y ii) Find the exact area of the surface…

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Q: State the type of the quadratic surface: (3)' + (4)° + (¿)* =1| 1. Ellipsoid 2. Hyperboloid of one…

A: Hence option 1) ellipsoid is correct According to the Bartleby guidelines I have to solve only first…

Q: Identify and sketch the section of the surface at x = 0. 2y² – x² + 2z? = 50 Type of the surface:…

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Q: The quadric surfaces y = z and 9z = 2x + 2y? intersect as shown above. %3D We can describe this…

A: Consider the quadratic surface: y=z2…

Q: 7. Consider the parametric surface S given by r(u, v) = 3u cos vi+ 3u sin vj + u? k, for 0 <u < 2,…

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

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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 by completing the squares. x + 4y? – 2 – 6x + 8y + 4z = 0 O An elliptic…

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Q: Consider the surface z = 4x2² + y² + 1. An equation for the tangent plane to this surface at the…

A: Given: z=4x2+y2+1

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: 3. Find an equation of the surface of revolution generated by revolving the given plane curve about…

A: Given, Curve,z=ex in the  xz-plane about the x-axis To find an equation of surface of revolution…