Find the equation of the surface of revolution generated by rotating the given curve about the specified axis. Construct the surface and represent it graphically. x² + z² + x² y² = 2z, i) ii) z² = 4, y = 0; x = 0 Z-axis Y - axis

Q: Describe and sketch the surface (x2/16) - (y2/9) + z2 = -1

A: The given surface x216-y29+z2=-1. We have to sketch the graph of the surface.

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

Q: Find the equation of the tangent plane to the surface z =9-(r² +y2) at the point (1,1,7). Write the…

A: Given surface is z=9-x2+y2⇒x2+y2 +z=9⇒x2+y2 +z-9=0 Take  fx, y, z= x2+y2 +z-9 And, Point say P is 1,…

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: 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: Find the Center and vadius of the following (X-2) +(y-3)=16 Circle equation The equatiun is in the…

A: We compare with the general form of equation of circle to get the center and radius.

Q: Find parametric equations for the line tangent to the curve of intersection of the surfaces at the…

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

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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: Identify the type of quadric surface defined by the equation x2 y + z = 1, 49 9. and find all x-,…

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Q: Sketch and identify the surface given by x2 + 4y + 4z2 = 0.

A: Equation of the surface is given by:x2+4y+4z2=0 we need to identity the surface and hence sketch the…

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…

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

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

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Q: Sketch the curve (x2 + y2 )3 =4x2y2 by converting to polar coordinate system

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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…