Sketch the surface given by the equation x2+z2/3+y=3 indicating the points where the surface crosses the x , y , and z axes.

Q: Identify and sketch the surfaces y = - (x2 + z2)

A: Given Data The equation of curve surface is y=-(x²+z²)   The sketch of the surface equation is,

Q: Describe and sketch the surface x + 2y + 3z = 6

A: Given

Q: Find an equation for the surface consisting of all points that are equidistant from the point…

A: The formula to find distance between two points is given below:

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

A:

Q: Find an equation for the surface generated by revolving the curve about the y-axis. y = 2x2 , (z =…

A: The distance of any points ( having same y co-ordinate ) on the curve is at same distance from…

Q: Find the surface are generated when y= (x^3)/5 is revolved about the x axis on the interval…

A: Explanation of the solution is given below...

Q: Consider the surface z = (x+ 1)² + (y – 2)² – 1 Does the point (1, 3, 1) belong to this surface?

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Q: Match the equation with the surface it defines:

A: given equation is x24+y24=z249

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

A: y2=16+x2+z2

Q: Sketch the surface z = f(x.y). f(x.y) = - /x² +y?

A:

Q: Find an equation for the surface consisting of all points that are equidistant from the point (-1,0,…

A: The given point and the equation of the plane from where all the points of the surface are…

Q: Sketch the surface with equation x^2 + y^2 + 2z^2 − 1 = 0.

A: The given equation is x2+y2+2z2-1=0

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: Find an equation which describes the surface created by rotating (r, x, 0) around the r-axis. Note…

A: Our Aim is to find an equation which describes the surface created byrotating (x,x,0) around the…

Q: Sketch and identify the surface given by the equation Z=: x² +

A:

Q: Find an equation of the surface obtained by rotating the curve y = 1- sqrt(z) (square root of z)…

A: Given the equation of curve, y=1-z This can be written as z=1-y On squaring both sides, z=(1-y)2…

Q: Find an equation of the surface of revolution obtained by revolving the plane curve 4x² – y² = 4…

A: The given equation of plane curve is 4x2-y2=4. Since the plane curve is rotated about x-axis,…

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: Write the equation for the surface generated by the revolving curve y = 2x +1, revolved around the x…

A:

Q: Write the equation for the surface generated by revolving the curve x2 - 2y2 = 1 about the y-axis.…

A:

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: Consider the equation of the surface. 1 f (x, y) = x² + y² + 1 Identify the graph of the surface…

A:

Q: Sketch the curve of intersection of the surfaces. The paraboloids z = x² + y² and z = 25 – x – y².…

A: Given that: z=x2+y2      ......(1)z=25-x2-y2      ......(2)

Q: Sketch the portion of the surface that lies in the first octant: y= z.

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Q: Use traces to sketch and identify the surface -x2+ 4y2-z2=4

A: To identify the surface, set each variable to some constant and find what type of surface produces…

Q: Identify the surface whose equation isľ = 3 sec (0). O Circle O Hyperbolic Paraboloid O Cone Sphere…

A:

Q: Sketch the section of the surface at y=0. z = /2+x² + y?

A:

Q: sketch the given surface. x2 + y2 − z 2= 1

A: Given: x2 + y2 − z 2= 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: Plot the surfaces over the indicated domains. Ifyou can, rotate the surface into different viewing…

A: The given equation is   z=x2+2y2at-1≤x≤1and-2≤y≤3

Q: Find an equation for the surface of revolution formed by revolving the curve in the indicated…

A:

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: find an equation for the surface generated by revolving the curve about y-axis. y = 4x2, (z = 0)

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

Q: Sketch the graph of the equation in xyz coordinate system and identify the surface 8x? + 4y? – z2 =…

A: Sketch the graph for the given surface.

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: Classify the quadric surface given by equation  and  determine its standard  form. x2 + y2 − z2 − 2x…

A: x2 + y2 − z2 − 2x − 4y − 4z + 1 = 0

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

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

Q: Find an equation for the surface of revolution formed by revolving the curve z2 = 2y in the yz-plane…

A: To find the equation for the surface of revolution

Q: Find an equation for the surface of revolution formed by revolving the curve 2x + 3z = 1 in the…

A: Our Aim is to find an equation for the surface of revolution formed by revolving the curve 2x+3z=1…

Q: Find the equation of the surface of revolution formed by revolving the curve 2x + 3z = 1 in the…

A:

Q: Plot the surfaces over the indicated domains. Ifyou can, rotate the surface into different viewing…

A: To Plot: Plot the surface over the indicated domains:z=y2-2≤x≤2-0.5≤y≤2

Q: The 2D curve 4x2 - y2 = 3, generates a surface in 3D by rotationing it out of the xy-plane and…

A: To answer it, let us go through the equation of Hyperboloid of 2 sheets   x2a2 - y2b2  - z2c2 = 1…

Q: 5. y-z =16

A: Since you have asked multiple questions in a single request so we will be answering only first…

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

A:

Q: Find an equation for the surface generated by revolving the curve about the y-axis. y = 2x , (z = 0)…

A:

Q: Use  inertia  to  classify  the  quadric surface  given by equation. x2 + y2 + 2z2 − 2xy − 4xz − 4yz…

A: We have to use  inertia  to  classify  the  quadratic surface  given by equation. x2 + y2 + 2z2 −…

Q: Describe and sketch the surface y = z2

A: Solution: Consider the given surface y = z2 On the y z-plane, it represents a parabola that opens in…

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

A: Used graphing calculator to graph:z = 1 + y^2 - x^2 from two viewing angles