Find the Vertex, Focus, Directrix, and Focal Width of the Parabola

question 161

Multiple Choice

Find the vertex, focus, directrix, and focal width of the parabola.
- $$\mathrm { y } ^ { 2 } = 32 \mathrm { x }$$

• A) Vertex: \(( 0,0 )\); Focus: \(( 8,0 )\); Directrix: \(x = - 8\); Focal width: 128
• B) Vertex: \(( 0,0 )\); Focus: \(( 0,8 )\); Directrix: \(y = - 8\); Focal width: 8
• C) Vertex: \(( 0,0 )\); Focus: \(( 8,0 )\); Directrix: \(x = - 8\); Focal width: 32
• D) Vertex: \(( 0,0 )\); Focus: \(( 8,8 )\); Directrix: \(x = 8\); Focal width: 128

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Definitions:

Consumer Surplus

The benefit consumers receive when they pay less for a product than what they were prepared to pay, measured by the area beneath the demand curve and above the price.

Monopolist

An entity, often a single firm, that holds exclusive control over the supply of a particular good or service, setting prices without competition.

Marginal Cost

The increase in cost that arises from producing one additional unit of a good or service.

Competitive Industry

An industry in which numerous producers supply a homogeneous product or service, leading to competition over price and quality.