Consider the surface z = (x+ 1)² + (y – 2)² – 1 - Select a correct name for this surface and point out the lowest point. A A circular paraboloid, (1, -2, 1) A cylinder, (-1, 2, –1) CA cylinder, (1, -2, 1) A circular paraboloid, (-1, 2, –1)

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

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Q: (2) : Graph the surfaces z = x² + 4y² and z = 1-4y² on a common screen using the domain x| < 1.2 ,…

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Q: Suppose we have a quadric surface described by 1 (r, y, z) | 1 1 = 7. 1 -4 Using canonical…

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Q: For a given surface z-x^2-y^2=10 Find the parametric representation of the straight line which…

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Q: Find the surface area for the portion of the surface f(x,y)=1-x² + y that lies above the triangular…

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Q: Example 8. Evaluate , A.n ds where A=(x+y)i-2j+2yzk and S is the surface of the plane 2x + y + 2z =…

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

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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: If A = 18zî – 12j + 3yk then find SS,A.ñds where S is the surface of the plane %3D 2x + 3y + 6z = 12…

A: Given, surface S: 2x+3y+6z=12           and                       A→=18zi^-12j^+3yk^

Q: Identify the quadric surface satisfying each of the given equations and then make a rough sketch to…

A: identify the quadric surface satsifying each of the given equations and make rough sketch to show…

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: Consider the following equation of a quadric surface. 2 x = 1-y -z a. Find the intercepts with the…

A: Given,  x=1-y^2-z^2

Q: A. Consider the quadric surface Q in R³ with the following equation: (x – 1)2 y? (z+ 2)? 1 - 25 4 16…

A: We will find traces by substituting values of x,y,z in given equation of surface . using traces and…

Q: I just need #36.

A: Given the equation

Q: A = xy'a, + y'a, + y°za, and S is the surface of the cuboid defined by 0 < x < 1, 0 < y < 1,0 < z <…

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Q: The parametric representation of the surface y2 - 4y + z2 = 0,0 < x < 3 is a) 7(u, v) = (v, 2 + 2…

A: solution:y2-4y+z2=0 , 0≤x≤3considery2-4y+z2=0∴y2-4y+4+z2=4∴y-22+z2=22

Q: Let (P) be the surface given by the following equation z = 5-x²-y² and (Q) be the surface given by…

A: Given surface P is, z=5-x2-y2    ----(1) For xy projection, put z=0 in (1) we get, 0=5-x2-y2⇒…

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: Let 13 be the surface with the equation given by 4x²-9y²= 9(z²+4)

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Q: Sketch the surfaces HYPERBOLOIDS (y2/4) - (x2/4) - z2 = 1

A: we have to sketch the surface of the hyperboloids  y24-x24-z2=1

Q: ify and sketch the

A: Given,       9x2+25y2-16z2=0

Q: 1. Let a, b, c ER and let Sa,b,c = {(x, y, z): ax2 + by2 + cz²=0, x² + y² +2²=1}- (1a) For which…

A: Given: Sabc=(x,y,z): ax2+by2+cz2=0, x2+y2+z2=1 To find: the values a, b, c for which Sabc a regular…

Q: For the surface 4x² + y² −z = 0, classify the indicated trace as an ellipse, hyperbola, or parabola.…

A: We have been given the equation  4x² + y² −z = 0           (1)

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: Let 13 be the surface with the equation given by 4x²-9y²= 9(z²+ 4)

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Q: Sketch the surfaces 1. . z = x2 + 4y2  2. x = 4 - 4y2 - z2 3. x2 + y2 = z2

A: The given surfaces are sketched using online 3D calculator.

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: Let I- (VxG) ndo, where G(x.y,z)=(ze*-y,4x,z*) and S is the part ofi the surface z=/x²+6y²+1 that…

A: Given that Gx,y,z=zex-y,4x,z4. The surfaces are given by z=x2+6y2+1⇒z2=x2+6y2+1 that lies inside the…

Q: Sketch the trace curves of x^2 − y^2 + z^2 − 4x + 2z = 4, and use these trace curves to sketch the…

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Q: Given the surface of z =10-4x² – y² : Sketch the surface of z=10-4x² – y² where z>0 and show the…

A: Given:-               z = 10- 4x2 - y2z = 10-- 4x2 + y2

Q: Locate and classify the stationary points on the surface z=xy2-2xy-2x2-3x, remembering that  x, y ,…

A: Solving for stationary points of given function using partial derivatives

Q: 1. Find a parametric representation for the surface: the part of the sphere x2 + y? + z2 = 4 that…

A: According to the given information, It is required to calculate the parametric representation for…

Q: Consider the surface x² - y² + z² = −4. A. Identify the name of the surface. B. The line…

A: We know general form of hyperboloid of two sheets is  -x2a2-y2b2+z2c2=1 where positive term is the…

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: Identify and sketch the section of the surface at z = 0. 17z = y – x Type of the surface: 6 4. 12 12…

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Q: Identify and sketch the section of the surface at x = 0. 25x? + 16y² – 9z² = 0 Type of the surface:…

A: We need to sketch the section of the surface x=0, 25x2+16y2-9z2=0. For x=0, 16y2-9z2=0. The graph is…

Q: (a) Find max, min or saddle points for the surface Z= x* - 3xy + 5x

A: We have to find first and second order partial derivatives.

Q: A trace of the surface +- z = 0 on the xy- plane is: O Point at (3, 2, 0) O Circle Ellipse Point at…

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: 5. Prove that the surface E, = {(x, y, z)|a² + y² = 4} is locally isometric to the surface E2 = {(x,…

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Q: Identify and sketch the section of the surface at z = 0. v2 = 1 25 4 16 Type of the surface: too 4 4…

A: Solve the given

Q: Consider the surface given by the equation z - y = x2. Draw a total of at least 3 traces in at least…

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Q: The parametric representation of the surface x2 -8x + z2 = 0,0 < y 5 5 %3D is a) (u, v) = (4 cos u ,…

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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: Here is a two-variable function: f (x, y) = Vx2 + y² – 1 This is the upper half of a quadric…

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Q: : The trace of the surface S x² Z = + 9. 4 in the plane z = 4 ||

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

A: Given equation is y2+z2=16

Q: Let S be the surface with equation 4y2 + 4z²x² - 16 -0. 1. Find an equation of the trace of S on…

A: Solution:S be the surface with equation 4y2+4z2-x2-16=0⇒4y2+4z2-x2=161)Traces of S in the coordinate…

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

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Q: 7. Sketch the surface 1≤z≤2-x² - y²

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