Find an Equation for the Surface Obtained by Rotating the Parabola

question 18

Multiple Choice

Find an equation for the surface obtained by rotating the parabola $y = 3 x ^ { 2 }$ about the $y$ -axis.

• A) \(z ^ { 2 } - 3 x ^ { 2 } - y ^ { 2 } = 1\)
• B) \(y ^ { 2 } + 3 x ^ { 2 } = z\)
• C) \(z ^ { 2 } - 3 x ^ { 2 } = y\)
• D) \(3 z ^ { 2 } + 3 x ^ { 2 } = y\)
• E) \(z ^ { 2 } + 3 x ^ { 2 } + y ^ { 2 } = 1\)

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Definitions:

Desensitization

Desensitization is a psychological process through which an individual is made less likely to feel extreme responses towards a stimulus, often used in the treatment of phobias and anxieties.

Systematic Desensitization

A method in behavioral therapy aimed at decreasing fear and anxiety by slowly introducing the individual to the object or situation that causes their fear.

Overgeneralization

A cognitive distortion where an individual concludes a general rule or pattern from a single event or a small number of events.

Free Association

A psychoanalytic technique where the patient speaks freely about their thoughts, memories, and feelings, revealing the unconscious processes.