Classify the Surface $$22 x ^ { 2 } + y ^ { 2 } - z ^ { 2 } - 2 y + 2 z = 0$$

question 83

Multiple Choice

Classify the surface. Select the correct answer.
$$22 x ^ { 2 } + y ^ { 2 } - z ^ { 2 } - 2 y + 2 z = 0$$

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

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Definitions:

Depolarization

The process in which the electrical charge of a cell membrane becomes less negative, often leading to the initiation of an action potential.

Repolarization

The process of restoring the negative charge inside the membrane of a neuron or muscle cell after depolarization.

Afterpotential

Afterpotential refers to the changes in membrane potential that follow an action potential in a neuron, often leading to either hyperpolarization or depolarization.

Threshold

The minimum level of stimulation required to trigger a neural impulse or a response in other signal-transmitting systems.