• Which of the following conics is a trace on one of the coordinate planes of the surface whose equation is given by a2 +y? + z2 – 6z – 16 = 0? a. x? – y? = 16 b. x? + (z – 3)2 = 25 c. x? + y? = 25 d. y? + (2 + 3)? = 25 %3D O a. b. С. d.

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: This exercise refers to the hyperbolic paraboloid z = y -x. (a) Find an equation of the…

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Q: Which of the following is simply connected? a) the horizontal strip Imz <1 b) the annulus 1</z <2 c)…

A: This is a problem of topology.

Q: Identify and sketch the section of the surface at z = 0. y? 2 Type of the surface: hyperboloid of…

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Q: Let C be the boundaries of the ellipse 49x2 + 9y? = 49 taken in the counterclockwise direction. A…

A:

Q: Let 3 be the surface with equation given by 4x² − 9y² = 9 (z² + 4). 1. Find an equation of the trace…

A: note : As per our company guidelines we are supposed to answer ?️only first 3 sub-parts. Kindly…

Q: (a) Consider the following. -5 5 5 -5 Identify the surface graphed. O cylinder O paraboloid O cone…

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Q: Question 9 Which surface has the following equation? a2-2y = 32 O Cylinder O Plane O Paraboloid O…

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Q: In the Euclidean plane with fixed cartesian system Oxy, let C be the conic defined by the equation…

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Q: y? dV, where T is the solid tetrahedron with vertices (0, 0, 0), (2, 0, 0), (0, 2, 0), and (0, 0, 2)

A: Given function f(x,y,z)=y2 Tetrahedron T is region with vertices (0,0,0), (2,0,0), (0,2,0) and…

Q: J. Let 3 be the surface with equation given by 4x² - 9y² = 9 (2²+4). 1. Find an equation of the…

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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,…

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: Match the ellipsoids shown in the figure above with t 1) x2 + 4y + 4z? = 16 2) 4x2 + y +4z? = 16 3)…

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Q: State the type of the quadratic surface: æ² + () + 2? = 1 1. Hyperboloid of two sheets 2.…

A: Solution ) given x2 + (y/8)2 + z2 = 1 We can write this equation  x2/12 + y2/82 + z2/12 = 1 the…

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: ssume you are given the surface S with equation æ² + + = 1. = 1. 9

A: We can use distance formula to solve the problem

Q: Given a plane 2y + 4z = 5 intersects the cone z^2 = x^2 + y^2 in an ellipse. Find the points on this…

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Q: The attached figure shows the surface S1: y + z= 2, limited in the first octant with surface S2: x =…

A: The area of a surface z=f(x,y) bounded by the region R is given by the integral expression:-…

Q: Identify the surface 2x² + 4y? – 1=0. A. An elliptic cylinder. B.Ahyperbolic cylinder. OC. None of…

A: We will solve the problem

Q: 3.) Consider the paraboloid z = 4+a + 3y?. Imagine releasing a ball from the point P (3, 4, 61) and…

A: We are given a paraboloid z = 4 + x2 +3 y2 .  Let f ( x, y ) =  4 + x2 +3 y2 In part (a) we need to…

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: 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: For which point y on the ellipsoid æ² + 2y² + 4z² =1 (shown below) is %3D the quantity x+ y+ z as…

A: Lagrange's Multiplier:- To find:- Extreme values of f(x, y, z)…

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

A:

Q: Let C be the boundaries of the ellipse +=1 taken in the 9 16 counterclockwise direction. A…

A: We have to check

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

A:

Q: (b) Find the equation of the tangent plane to the hyperboloid r2 + 3y? – 322 = 1 at the point (1,…

A: We have to find the equation of the tangent plane to the hyperboloid x² + 3y² − 3z² = 1 at the point…

Q: Calculate | [(a* – 3y) dæ + (2y³ + 4x) dy] wherein y(t) = (3cos(t), 3sin(t)), 0 <t < 2ñ, is an…

A: Please check step 2 for the solution.!

Q: 2. The plane r + y +2z = 2 intersects the paraboloid z = x² + y² in an ellipse. Find the points on…

A: According to the given information, it is required to find the nearest and farthest distance from…

Q: Identify a generating curve on the xz-plane for the surface of revolution with equation a² + y? + 2?…

A: Consider the surface of revolution with equation, x2+y2+z2=e2x it is required to find the generating…

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: The surface z? = x² + y? – 4x + 5 remains unchanged when rotated about the line L in R Which of the…

A: The given surface is z2=x2+y2-4x+5, which is as shown below: This is a hyperboloid paraboloid.…

Q: Sketch the following surface: (z+4)² + (y-1)² = 1 a.) Draw the projection on a xy plane Show…

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Q: Let = 1. a2 be a hyperboloid of one sheet. a) Find the equation of the tangent plane at a generic…

A:

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: Is it true or false that by using a suitable translation x = x' + xo, Y = y' + Yo, it is possible to…

A: Transforming the conic equation

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

A:

Q: What are the z-traces of the surface x2+ y2+ z=5? O a. Circles. O b. Ellipses. O. Hyperbolas. O d.…

A: here we have to find z- traces and x- traces of the given equation.

Q: 11. The equation of a sphere with center at (-3, 2, 4) and of radius 6 units is? a. x² + y² + z²…

A: Equation of sphere is (x-h)2+(y-k)2+(z-l)2=r2. Where (h, k, l) is coordinates of the center.

Q: Find the area of the surface generated by removing about the x-axis the upper half of the ellipse…

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Q: This exercise refers to the hyperbolic paraboloid z = y? – x². (a) Find an equation of the…

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Q: Evaluate |(y zi+y°i+xzk)•d$ where S is the boundary of a cuboid defined by S -15x<1, -1<ys1 and…

A: The given integral: S=∬s(y2zi→+y3j→+xzk→) dS Where S is the boundary of cuboid defined by -1≤x≤1,…

Q: 2. Find the area of the ellipse S on the plane 2x + y + z = 2 cut out by the cylinder x2 + y? = 2x;…

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Q: Find the area of the surface generated by removing about the x-axis the upper half of the ellipse…

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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…