For the quadric surface x2 – y? + 22 = 9: - (a) Find the trace for x = k (your answer must have k). What shape is it? (b) Find the trace for y = k (your answer must have k). What shape is it? (c) Find the trace for z =k (your answer must have k). What shape is it?

Q: 2. State the names of the following quadric surfaces. (a) The surface z = y² – 2x². (b) The surface…

A: a. this equation is in form of  as sign of A and B is opposite it is  Hyperbolic paraboloid

Q: Q3: Find the points on the surface x^2+z^2-5=D0, closest to the origin.

A: see the attachment

Q: ) I would eed help to dentify the surface whose equation is given below, please?  2r^2 + z^2 = 1

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Q: 8.2

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

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

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Q: sketch the given surface. x 2+ 9y 2 + 4z 2 = 36

A: To sketch the given graph

Q: For the surface 4x² – y² + z² = 9, the trace y = 0 is : O Ellipse O Elliptic cone O Hyperbola O…

A: Topic = Geometry The trace is Ellipse.

Q: Which of the following quadratic surfaces describe an elliptic paraboloid shape ? OA. z = 2? – y² +…

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Q: Use traces to sketch and identify the following surface 25x² + 4y? + z² 100.

A: Given: The surface 25x2+4y2+z2=100.

Q: Q3: Find the points on the surface x^2+z^2-6=0, closest to the origin.

A: The distance of the point on the surface is given by d=x2+y2+z2. To obtain the distance insert the…

Q: For the surface 4x² +2²-y²=9, classify the trace when z = 1. O line O hyperbola O ellipse O parabola

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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: Q3/ Examine the following surface for maximum and minimum points z = 2x2 + 3xy + 4y² – 5x + 2y

A: Since you have posted multiple question according to company rule we are supposed to give solution…

Q: Q3: Find the points on the surface x^2+z^2-630, closest to the origin.

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Q: Given surface A₁: x = 2√y + 1 and sphere A₂: x² + y² + z² − 16x + 6y − 4z + 76 = 0 1. Sketch surface…

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Q: 18. Find the surface area of the part of the sphere x² + y² + z² = 4 that lies inside the cylinder…

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Q: Find the center C and the radius r of the sphere S: x2 + y? +z2 + 4x + 8y- 8z =-11

A: General equation of sphere  (x-h)2+(y-k)2+(z-p)2 = r2  center (h,k,p)  radius = r

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: 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: Choose the equation that represents the * graph of the cylindrical surface below -25 -20 -15 -15 -10…

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Q: Consider the surface 4a? – y? + 2z² + 4 = 0. a. Find the value(s) of k such that the cross-section…

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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: 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: For the surface described by z= - 20y+x² – 10x +3y-2xy | a. At what point are both zx=0 and zy=0 %3D…

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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: 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: (a) What does the equation x² + y´ = 1 represent as a curve in R? (b) What does it represent as a…

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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: Q3: Find the points on the surface x^2+z^2-2=0, closest to the origin.

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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: 9. Reduce the following equation to one of the standard forms, classify the surface, then sketch the…

A: General equation of an ellipsoid is given by, (x-p)²/a² +(y-q)²/b² +(z-r)²/c²= 1

Q: Consider the following equation of a quadric surface. 4x? + 16y? + 16z? = 64 a. Find the intercepts…

A: The graph of the given surface is given as follows :

Q: x2 Consider the surface T with equation 4 (y – 3)² + 22 = 1. - 3

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Q: Q3/ Sketch the surface z 3x2 + y? +1 and find its linear approximation at P.(0,-1).

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Q: Match the equation with the surface it defines. Also, identify each surface by type. 1. x = y? - z2;…

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Q: (a) x² + 2x + 4y² + 16y + 9z? 19

A: Sketch and identify the surfaces: (a) x2+2x+4y2+16y+9z2=19.

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

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Q: Match the equations of the surface with the graphs below. A в D E F 1. 9a? + 4y? + z² = 1 2. a2 +…

A: now identifying the given quadratic surface

Q: Sicatch the section of the surface at y-0. 2r +z = 6 AM -8-6-4 -2 -8-6 -4 -2 2 N 6

A: Here y=0 so graph is form in xz plane This is the equation of line in xz plane For x intercept we…

Q: Find the surface area generated by rotating the semi-circle x = (49 – y² be- tween -7 < y < 7 about…

A: To Determine :-  The surface area generated by rotating the semi-circle x = 49 - y2 between -7 ≤y ≤7…

Q: Which surface below is an elliptic paraboloid? O x^2 + y^2/4 - z^2 = 1 O z = -sqrt(x^2 + y^2) z =…

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Q: 28 Describe the surface withe cylindrical equabion p?+z?=9. [ Oraw it and Solve it] .

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Q: Q3: Find the points on the surface x^2+z^2-16=0, closest to the origin.

A: The equation of the surface is x2+z2-16=0.

Q: Q2 Find the maXimum and minimum values of aFunction FCXS.2) = 8x+j+ 2 en the Surface x+y, z"=18 %3D

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Q: The perimeter of an ellipse is given by P = 4a V1-k-sin-8 de where, k = Using the Simpson's rule,…

A: The given equation of the ellipse is: x242+y272=1 Result: The standard form of the ellipse is:…

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

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

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