# is Find an equation for, and identify, the surface that results when the surface x2 -... is Find an equation for, and identify, the surface that results when the surface x2 - y2 – 2z2 reflected about the plane Y = 2. b) Find an equation for, and identify, the surface that results when the surface x2 – 4y2 + x2 = ( is translated to the point D(2,-1,-4).

The given equation can be rewritten as : which is the equation of a hyperboloid of one sheet along the x- axis, like one in the picture: Reflecting this surface about the plane will result in the same surface , since the surface is symmetric about the plane . Hence the resulting equation will be or (b) The given equation can be rewritten as: which is the equation of an elliptic cone with axis y-axis. Translating the origin to D, we get the equation: which is the equation of an elliptic cone with centre D

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