Consider the quadric surface a² +²2=1. Answer the following questions. (a) What type of quadric surface is described by the equation? (b) Write an equation for the similar quadric surface which has its axis of rotation parallel to the y-axis and is center at the point (3, 1,-2).

Q: 1. Identify the quadric surface 2. Write the equation of the traces of the quadric surface on the…

A: The equation is of form  y2-z23-x212=1  This gives a quadric surface called Hyperboloid of two…

Q: Project: S is a surface in R° with equation x² +y² – z² = 1. The point P (2,1,2) lies on this…

A: Clearly : x-z = 0 and y+1 = 2. So, we can write: 1.(x-z) = 0.(y+1). So, L1 can be written…

Q: Identify the surface whose equation in rectangular coordinates is given by x² + y²-2²-4x-6y+12=0.…

A: Given x2+y2-z2-4x-6y+12=0 ∴x2+y2-z2-4x-6y+12=0⇒x2-4x+4+y2-6y+9-z2=1⇒x-22+y-32-z2=1 The equation of…

Q: A particle traveling around the circle (x-2)^2 + (y-1)^2 = 49. Write parametric equations for each…

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Q: Match the equation with the surface it defines.​ Also, identify the surface by type​ (paraboloid,…

A: Standard equation of elliptic cone    Given equation :

Q: Find the equation of the surface of revolution that is generated by rotating the straight line y = x…

A: The surface of revolution that is generated by rotating x=f(y) around the y-axis is x2+z2=f(y)2 so…

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: Write the equation of the sphere with centre at ( 0,0,0) and radius = 2

A: The center of the sphere is:(h, k, j)=(0, 0, 0)The radius of the sphere is:r=2

Q: 19. Identify the surface whose equation in rectangular coordinates is given by x² +…

A: Given equation is x2+y2-z2-4x-6y+12=0 ∴x2+y2-z2-4x-6y+12=0⇒x2-4x+4+y2-6y+9-z2=1⇒x-22+y-32-z2=1 We…

Q: 9) Sketch the graph of the equation y² +2²=1 and correctly identify the surface.

A: Given: The equation is y2-x24+z2=1. To sketch: The graph of the given equation. To identify the…

Q: Consider the surface defined by the equation 2.x2 – 2y2 – z = 0. (a) Choose any one of the variables…

A: The equation is the form z=f(x,y) represents a surface in the space. In this problem the equation of…

Q: 2 y² - x² = 9 a) Sketch the graph of the equations in three dimensions and identify the surfaces.

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

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Q: Write your answer on a piece of paper with your name on it. Snap a picture, then upload your answer.…

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Q: Let S be the quadric with equation 36x² – 4y? – 9z2 – 36x = 0 - - (a) Classify the graph of S. (b)…

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Q: -t sin 4t -t sin 4t

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Q: The paraboloid z = 8-x-x²-3y2 intersects the plane x = 2 in a parabola. Find parametric equations in…

A: The equation of the paraboloid is given as z=8-x-x2-3y2. The paraboloid intersects the plane x=2 in…

Q: iven: surface Q : 9x² – 4z² = 9y a) Give the equation of the trace of Q on each coordinate plane and…

A: Given Q: 9x2-4z2=9y

Q: the indicated coordinate plane about the given axis. Equation of Curve Coordinate Plane Axis 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: (r – 1)? + (y + 2)² + (z – 1)² = 49

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Q: Sketch the graph of the plane 3r-y+2z+6=0. of the plane. 2 Sketch the graph of the surface z = 4-4x2…

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Q: 6. Sketch the graphs of the following equations and identify the surface: (a) x² - 16y² = 4:² (b)…

A: (a) The equation x²- 16y²= 4z² is the equation of an hyperboloid of one sheet. To visualize the…