#$&* course Mth 277 6/22 11 pm query_09_7*********************************************
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Given Solution: &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): ------------------------------------------------ Self-critique rating: ********************************************* Question: Identify the quadric surface given by the equation 8z^2 = (1/8) + (x^2)/9 + (y^2). Describe the traces in planes parallel to the coordinate planes (and sketch the graph). YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: This quadric surface is a one sheet hyperboloid. The intersection of the hyperboloid with planes parallel to the two primary planes form ellipses with varying axes. confidence rating #$&*: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): ------------------------------------------------ Self-critique rating: ********************************************* Question: Describe the quadric surface given by the equation ((x-3)^2)/2 - ((y-1)^2)/4 - (z^2-2)/9 = 4. YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: This surface is a two sheet hyperboloid, with vertices at (3,1,5) and (3,1,-1). confidence rating #$&*: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): ------------------------------------------------ Self-critique rating: ********************************************* Question: Describe the curve intersection of the two quadric surfaces 4z = (y^2)/9 - (x^2)/16 and (x^2)/4 + 2(y^2) - 4(z^2)/3 = 1. YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: 4z = (y^2)/9 - (x^2)/16 describes a hyperbolic paraboloid centered around the origin. x^2/4 + 2y^2/2 - 4z^2/3 = 1 describes a one-sheet hyperboloid centered around the origin. A slice of the first graph would give us an ellipse, and a slice of the second would give as a parabola. Therefore, it makes sense that an intersection of the two would yield a elliptic paraboloid. confidence rating #$&*: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): Most of this was touch and go, it's a little difficult to visualize the 3D objects in my head. I tried drawing out each pair of axes (XZ, YZ, XY) and combining them, and that was helpful when determining what kinds of quadric surface each was. ------------------------------------------------ Self-critique rating:"