Sketch the quadric surface: r +4y2 +4z2 16. Note: The x, y, & z axes are depicted in red, green, & blue, respectively.

Q: determine the type of the quadric surface. ) + G)° + 2:² = 1

A: To determine the type of quadric surface(x3)2+(y4)2+2z2=1

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

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Q: The surface described by the conditions 2 + y? + z² = 4, x 0 is the same as the surface described…

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Q: Find an equation in cylindrical coordinates for the surface represented by the rectangular equation.…

A: Given rectangular equation is y = x2

Q: Find an equation in cylindrical coordinates for the surface represented by the rectangular equation…

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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: x² y? + z = 1 4 9.

A: Given equation  x^2/9 - y^2/4 +z = 1 this is equation of hyperbolic Paraboloid.  Quadratic Surface…

Q: Reduce the equation to one of the standard forms, classify the surface, and sketch it…

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Q: 2.a. Write the equation of the surface r? + y? = 4y in cylindrical coordinates. b. Classify the…

A: To convert to the cylindrical coordinates, we need to make the following substitutions: x=rcos(θ);…

Q: Classify the quadric surface. 22 = x² + y? + 1 81 ellipsoid elliptic cone ollintio naraboloid

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Q: Sketch the portion of the surface that lies in the first octant: x = y. 12 1.5 1 0.5 0.15 . 0. . 2.

A: The given plane is in first octant and the plane is given by:  x = y

Q: Sketch the surface created by 4.r2 + 9y? + 3622 = 36. %3D

A: Given,4x2+9y2+36z2=36 Simplify equation (i) as x29+y24+z21=1  .....(i) Intercepts along x,y,z…

Q: state the type of the quadric surface and describe the trace obtained by intersecting with the given…

A: x2+y42+ z2=1,y=5x2+y42+ z2=1

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: Simplify and identify the quadric surface, given: 9x – 18x + 4y² + 16y – 36z + 25 = 0

A: The given function is- 9x2-18x+4y2+16y-36z+25=0

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

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

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

A: given  -x2+9y2-z=0

Q: Find an equation in cylindrical coordinates for the surface represented by the rectangular equation…

A: Given:y2=10-z2r2=x2+y2x=r cosθy=r sinθz=z

Q: Which of the shapes below can make a regular tessellation of the plane?

A: there are only three regular polygons for tessellation and they are equilateral triangle, square and…

Q: Use  inertia  to  classify  the  quadric surface  given by equation. y2 − z2 − 9x − 4y + 8z − 12 = 0

A: We wish to use inertia to classify the quadric surface given by the following equation:  ------(1)…

Q: Determine the projection of the surface – y? = z on the yz-plane? (Hint: a = 0) Circle O No answer…

A: The solution is :

Q: Classify the surface: 1- x = 3y? + 4z2 O Plane O sphere O cone O Elliptic paraboloid O Ellipsoid

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Q: use polar coordinates to find the voluyme of the solid enclosed by the hyperboloid: -x2-y2+z2=1 and…

A: Given : Hyperboloid : -x2-y2+z2=1 Plane : z = 2 Rearranging equation of hyperboloid…

Q: Find a parametric representation for the surface.

A: To find a parametric equation we have to convert cartesian coordinate to spherical coordinate…

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: Q2: A cube of edge 24mm is resting on the top of a frustum of cone of base diameter 60mm and top…

A: We are asked to draw the isometric view of the solid.

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

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Q: Determine the intersection of the hyperbolic paraboloid z = (y2/b2) − (x2/a2) with the plane bx + ay…

A: Given The hyperbolic paraboloid equation is z=y2b2-x2a2 and the plane bx + ay − z = 0 .

Q: What is the highest point on the ellipse that is the intersection of the plane z+y+ 2z = 2 and the…

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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: 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: ify and sketch the

A: Given,       9x2+25y2-16z2=0

Q: Write down the parametric equetions |3D 4=6-t in cartesion Form

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Q: sketch the given surface. y 2+ z 2 = 1

A: To sketch: The surface y2+ z2 =1 Concept used: The general equation of the cylinder whose base…

Q: Determine the projection of the surface - y = z on the xy-plane? (Hint: z = 0) O Hyperbola O Ellipse…

A: projection of the surface

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: What is the highest point on the ellipse that is the intersection of the plane z +y+ 2z = 2 and the…

A: I am going to solve the given problem by using the Lagrange's Multiplier method to get the highest…

Q: a. z? -y? -x?+ 4x= 5 by-3 = x?+z² 2

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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: Sketch the surface in R' of the equation presented. 4x² + y? = 36 Interactive 3D Graph - 10…

A: The given equation is, 4x2+y2=36x29+y236=1x232+y262=1⋯⋯1 In 2D, equation (1) is a equation of a…

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: Classify the quadric surface. −49x2 + y2 + z2 = 49

A: Given query is to find the shape of the surface.

Q: Find an equation in cylindrical coordinates for the surface represented by the rectangular equation…

A: we have to find an equation in cylindrical coordinates for the surface represented by the…

Q: Sketch the portion of the surface that lies in the first octant: y = z. 0.15 0.a 0.1 0. 0.15 0.18

A: To sketch the portion of the surface y=z that lies in the first octant. The sketch of y=z is:

Q: Prove that the surface of the given equation is an ellipsoid. Hence, determine its center. 9x +4y…

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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…

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Q: Parametrize the intersection of the surfaces using t = z as the parameter. (If there are multiple…

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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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