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:

Fertilization

The process by which male and female reproductive cells (gametes) join to form a new cell that will develop into an embryo.

Zygote Splits

The process through which a zygote (fertilized egg) divides, leading to the development of twins in the case of complete division into two separate entities.

Fallopian Tube

A pair of tubes along which eggs travel from the ovaries to the uterus in the female reproductive system, playing a key role in fertilization.

Artificial Insemination

A means of conception in which sperm are injected into the vagina by a means other than sexual intercourse.