\text { Consider the surface } z^{2}-\frac{x^{2}}{4}-y^{2}=1 (a) Find equations for the traces listed below, and identify these curves as ellipses, hyperbolas or parabo-las. Then sketch the curves, showing their vertices and, for hyperbolas, their asymptotes. (b) Sketch the surface from part (a) showing the trace curves I=0, y=0, and z=2. And identify the surface by clearly mentioning its name. (i) 1=0(ii) y=0(iii) z=2

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