Classify the Surface $$25 x ^ { 2 } + y ^ { 2 } - z ^ { 2 } - 2 y + 2 z = 0$$

question 26

Multiple Choice

Classify the surface.
$$25 x ^ { 2 } + y ^ { 2 } - z ^ { 2 } - 2 y + 2 z = 0$$
Select the correct answer.

• A) A hyperboloid of one sheet with center \(( - 3,0,1 )\) and axis parallel to the \(z\)-axis.
• B) A circular paraboloid with vertex \(( 0,3,1 )\) and axis the \(z\)-axis.
• C) A cone with axis parallel to the \(z\)-axis and vertex \(( 0,1,1 )\).

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