Consider the following surface: z = x2 - (y2 / 4).  By hand, without any graphical utilities, find an equation for the intersection of the surface and a plane containing the points (1, 0, 0), (2, 4, 0), and (-1, -1, -1).

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.

Q: Find

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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: 1. For 3x - 5y? – 10z? = -30 (a) Identify the type and describe the quadric surface. (b) Calculate…

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Q: Find the point at which the line (-3, 3, 0) + t(-2, –3, –2) intersects the plane -2x – y + 3z = 5.

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

A: On solving this we will get

Q: Reduce the equation to one of the standard forms, classify the surface, and sketch it. (a) z23x²+4y²…

A: We have to reduce the equation in standard form, classify the surface and sketch the surface.Note:…

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…

Q: Write the standard equation for 4x 2 - 9y 2-36z =0. Identify the surface: a. b. C. d. 2. Escriba la…

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Q: Find an equation of the plane that passes through the line of intersection of the planes ( x – z = 1…

A: We have found the plane that passes through the line of intersection of the planes x-z=1 &…