Given -2-x2 -,2 = 1 (a) Write the equation above in standard for (b) Identify the surface. (c) What is its axis? (d) Sketch the surface.

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: Identify the surface defined by the following equation. 2x-y²-z² =0

A:

Q: Identify the surface with equation 9x2 – 4y?+ 16z2 – 144 = 0.

A: Given: The equation 9x2-4y2+16z2-144=0 To find: The name of type of surface with the given equation.

Q: Reduce the equation to standard form, classify the surface and sketch it     x2 = 2y2 + 3z2

A:

Q: sketch the section of the surface

A:

Q: Choose the equation that represents the graph of the quadric surface below 3. 21 O z = 4 - 5y2-92 O=…

A: From graph we see that the quadric surface represents a paraboloid whose axis is y-axis Here 1st…

Q: Find an equation for the surface consisting of all points P for which the distance from P to the…

A: Let, P(x, y, z) be the point on required surface.

Q: 22. z = 8 – x² – y?

A: To determine the sketch of the function.

Q: Describe the relationship between the graphs of the quadric surfaces x2 + y2 - z2 + 2z = 1 and x2 +…

A: Given: The quadratic surfaces,   To describe the relationship between given two graphs and to state…

Q: Describe and sketch the surface 4x2 + y2 = 4

A:

Q: What are the traces of a surface? How do you find them?

A: Traces of surfaces are curves that represent the intersection of the surface and the plane given by…

Q: Sketch the graph of quadratic surfaces. Y=(x^2+3z^2)^(1/2)

A: We need to plot the surface: y=x2+3z2.

Q: Find an equation for the surface obtained by rotating the parabola y=2 about the y-axis.

A:

Q: 4d. z =-x´ + y´ Name of the surface

A: The structure obtained from the given equation is more like of dome structure

Q: EXAMPLE 2 Describe and sketch the surface in R3 represented by the equation y = 6x.

A: Given equation : y = 6x in R3

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: Find the quadratic surface and sketch the graph of r+y +- 4xyz = 1

A: The given equation is: x2+y2+z2-4xyz=1

Q: By first writing the equation in standard form, identify the traces of the surface given by the…

A: Given equation:                           x2+3y2-6y+z2+4z-3=0

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: Identify the type of surface represented by the given equation.

A: Since we are given x25+y28-z22=1 -(i) and for finding the nature of surfacewe will solve for z.

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

A: We need to plot the surface over the indicated domains. We have to rotate the surface into different…

Q: Given 4x = 3y + 3z2 (a) Write the equation above in standard form. (b) Identify the surface. (c)…

A: As per the guidelines we are only supposed to answer three subparts , for next parts please ask…

Q: Identify the surface whose equation is given.

A: ρ cos Φ =1  -> z = 1 ( as we know in spherical coordinates z = ρ cosΦ)

Q: Identify and sketch the section of the surface at x = 0. 2y? – x + 22 = 50 Type of the surface:

A: This question is related to conic section .solve in step 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: Explain what it means for a surface to be orientable.

A: They are the surfaces for which we can define clockwise consistently. e.g. Cylinder and spheres are…

Q: Classify and sketch the surface x − y2 − 4z2 = 0.

A: The surface is given as x-y2-4z2=0. Rewrite the equation x-y2-4z2=0 as follows. x-y2-4z2=0x=y2+4z2…

Q: Identify the surface defined by the following equation. y 2 x2 Z= 10 16 The surface defined by the…

A: The given surface represents a Hyperbolic parabola.   A hyperbolic paraboloid is represented as…

Q: Reduce the equation to one of the standard forms, classsify the surface,and sketch it. x2 - y2 - 4x…

A: Given : equation x2-y2-4x-2z+3=0To find : reduce the equation in standard form, classify the surface…

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: 2. -1 -2 Identify the equation of the surface. = 1

A: Note: We are entitled to solve only one question at a time. As the specified one is not mentioned,…

Q: Sketch the surface given by the equation x2+z2/3+y=3 indicating the points where the surface…

A: Sketch the surface given by the equation x2+z2/3+y=3   indicating the points where the   surface…

Q: Identify and sketch the surfaces z = - (x2 + y2)

A: Identify and sketch the surfaces z = - (x2 + y2)

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

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

Q: Plot the surface of 6a2- 2x4- y?z2 = 0, for -10 <x, y, z < 10

A:

Q: II. Solve the following. Slems. 1. 2. Name and sketch the graph of the surface with equation +z2 –÷=…

A: Given

Q: Describe and sketch the surface 16x2 + 16y2 − 9z2 = 0

A: Given surface 16x2+16y2-9z2=0

Q: Choose the equation that represents the graph of the quadric surface below 3 O y = 4 – 5x² – 922 O I…

A: We have given a quadric surface. It is asked to find the equation of the surface from the given…

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

A: Express the equation 4y2+z2-x-16y-4z+20=0 in terms of the complete squares of y and z, and then…

Q: Identify and sketch the graph of the quadratic surface 4x2-y2-z=1

A:

Q: Identify and sketch the section of the surface at x = 0. 4 Type of the surface: 6. 6- 2 -8 -6 -4 4 6…

A: Given the surface

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: Given 4x2 + 9z2 = 9,2 (a) Write the equation above in standard form. (b) Identify the surface. (c)…

A: We have to  write the equation in standard form, name the surface, find its axis, sketch the…

Q: 5. y-z =16

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

Q: Q1/ Use traces to sketch and identify the surface z2 - 4x2 - y² = 4

A: Let's find.