Find an equation for the surface obtained by rotating the line z = 7y about the z-axis.

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: 32²+62-4x-3y+2=0. 1. identify the surface: Present a well-defined sketch of the surface.

A: Given, the surface               2x2-3z2+6z-4x-3y+2=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: Determine the surface area of the solid obtained by rotating the following parametric curve about…

A: Given: x=9+t2, y=2t, 0≤t≤2

Q: Identify and sketch the surface 9x² + y² − 2z² — 18x - 4y - 12z - 9 = 0. - Explain the position and…

A: The given surface is: 9x2+y2-2z2-18x-4y-12z-9=0. The given equation can be written as:…

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

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Q: Find parametric equations for the line in which the planes, X+2y-2z=5 and 5x-2y-z=0 intersects. Show…

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Q: Find parametric equations for the line in which the planes x + 2y + z = 1 and x - y + 2z =-8…

A: x + 2y + z = 1 and x - y + 2z =-8 are the two planes.Let z=t So, the equations become:

Q: what type of quadric surface is the following: y² - (z²/3) = 1 + (x²/12) write the equation of its…

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Q: Identify the type of quadric surface defined by the equation and find all x-, y-, and z-intercepts…

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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: 2. Consider the surface + + = 1. (a) On three different coordinate axes, sketch the slices of this…

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Q: Given the surface of revolution with equation 22 y? 3x. 3 3 Find a generating curve of the surface…

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Q: Consider x² y² 100 25 the following equation of a quadric surface. . Find the intercepts with the…

A: The given quadratic surface is (a)Find the intercepts with three coordinate axes If they exist as…