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

question 102

Multiple Choice

Find the vertex, focus, directrix, and focal width of the parabola.
- $$- \frac { 1 } { 40 } x ^ { 2 } = y$$

• A) Vertex: \(( 0,0 )\); Focus: \(( 0 , - 10 )\); Directrix: \(y = 10\); Focal width: 40
• B) Vertex: \(( 0,0 )\); Focus: \(( 0,10 )\); Directrix: y \(= - 10\); Focal width: 10
• C) Vertex: \(( 0,0 )\); Focus: \(( - 20,0 )\); Directrix: \(x = 10\); Focal width: 160
• D) Vertex: \(( 0,0 )\); Focus: \(( 0 , - 10 )\); Directrix: \(y = 10\); Focal width: 160

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Definitions:

Market Economy

An economic system in which decisions on production and consumption are based on voluntary exchange in markets.

Incentives

Factors, monetary or otherwise, that motivate individuals or businesses to act in a certain way, typically to achieve certain goals or outcomes.

Society's Welfare

The overall well-being and quality of life of a community or society, often considered in terms of health, happiness, and prosperity.

Efficiency

The degree to which resources are utilized effectively to achieve a goal with minimum waste of time and effort.