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

Q: Determine the projection of the following surface on the xy plane *- y+ =1 O parabola ellipse O…

A: To determine the projection of the given surface on the xy-plnae.

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: Show that the ellipse x = a cos t, y = b sin t, a 7 b 7 0, has its largest curvature on its major…

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Q: Find a parametrization of the hyperboloid of two sheets (z2/c2) - (x2/a2) - (y2/b2) = 1.

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Q: Draw a sketch of the plane of 4x – 4y + 2z – 9 = 0.

A: Solution

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

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

A: It can be solved in 2nd part using simple geometry.

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

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Q: Identify the quadric surface with equation -a + 9y? – z = 0. O elliptic paraboloid O hyperbolic…

A: given  -x2+9y2-z=0

Q: If (a,B.y) is a point at which the surface x2+y2-z²-2x+12=0 has a horizontal tangent plane, then y|…

A: As per guidelines, we will solve first question only. Let α,β,γ be the point on the surface…

Q: Sketch the xy-trace of the sphere whose equation is (x−3)2 +(y−2)2 +(z+4)2 =52.

A: We can find the xy trace by setting z = 0 in the original equation.

Q: Consider the three-dimensional Euclidean space with coordinates x, y and z. The intersection of the…

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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: Find parametrizations The portion of the paraboloid z =-(x2 + y2)/2 above the plane z =-2

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Q: Find an equation of the surface consisting of all points P(r, y, z) that are twice as far from the…

A: To find an equation of the surface whose all points are twice as far from the plane z=-4 as from the…

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: 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: classify the quadric surface given by equation and determine its standard form.x 2 + y2 − z2 − 2x −…

A: The given quadric surface is  x2+y2-z2-2x-4y-4z+1=0 To reduce to its standard form,…

Q: Determine the projection of the following surface on the plane of the xy-axes -2y? + + =1 3 3 O…

A: -2y2+x23+z23=1To find the projection

Q: In three space, find the parametric equations of the curve C of intersection of the cylinder S: x2 +…

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Q: Find a parametric representation for the lower half of the ellipsoid 5x² + 4y2 + z² = 1.

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Q: Given the curve of intersection of the x² + 4y² -z = 0 which is a paraboloid and the plane 2x - z =…

A: Solution:-

Q: (B) Integrate paraboloid (x, y, z)=- 2x-²-2-0 by the plane x=1. over the surface cut from the end of…

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Q: Put the quadric surface equation 4X (-8y + 4Z+39 = 0 into one of the standard forms, specify the…

A: The given quadric surface equation is           4x2+y2-z2-24x-8y+4z+39=0 Write the like terms…

Q: Let C be an ellipse in a horizonal plane lying above the xy-plane. Which type of quadric surface is…

A: Given, Let C be an ellipse in a horizontal plane lying above the xy-plane.

Q: Find a set of parametric equations for the curve of intersection of the paraboloid r² + 4y² -z = 0…

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Q: Find the vector equation that represents the curve of intersection of the paraboloid z = 4x² + y²…

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Q: Find the point on the curve of intersection of the paraboloid x² • y² + 2z=4 and the plane x-y+ 2z…

A: This question can be solved by options because we have only two equations and three variables.

Q: Does every second-degree equation in x, y, and z represent a quadric surface? Explain.

A: the equation of a quadric surface in space is a second degree equation in three variables. The…

Q: Find the surface which intersects the surfaces of the system z(x+ y) =c(3z+1) orthogonally and…

A: To finding the surface which is intersecting given system and orthogonal to circle is given as…

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: ). Find a parametric representation for the line of intersection of the following two planes: I - y…

A: We use cross product to find the direct vector for the line.

Q: let C be the curve of intersection of the 3-D graph of x2=2y (a "parobolic cylinder") with the graph…

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Q: Determine the projection of the following surface on the xz plane -y+ 름 =1 O Ellipse O Parabola O…

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Q: The part of the surface z =1  + 3x+ 2y 2 that lies above the triangle with vertices (0, 0), (0, 1)…

A: Part of the surface: z=1+3x+2y2∂z∂x=3, ∂z∂y=4yVertices of the triangles are (0,0) , (0,1) , (2,1)

Q: Describe and sketch the surface in R3 represented by  a. 2x+z=3 b. z=cos y

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Q: If A = 18zî – 12ĵ + 3yk then find Jſ, A.ñ ds where S is the surface of the plane %3D 2x + 3y + 6z =…

A: Note "As per our company guidelines we are supposed to answer ?️only first question. Kindly repost…

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 part of the surface z-1+ 3x + 2y that lies above the triangle with vertices (0, 0), (0, 1). and…

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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: Graph the surface 1 = y2 + z2 –- by first sketching at least three cross sections in each of the xy…

A: We have to sketch the graph of the following surface in the 3D space: . First we have to sketch the…

Q: Use traces to sketch and identify the quadric surface z² = x² +.

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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.