Find an Equation of the Line That Is Tangent to the Circle

question 22

Multiple Choice

Find an equation of the line that is tangent to the circle x ² + y ² = 25 at the point P ( 3, 4 ) .

• A) \(y = \frac { 3 } { 4 } x + \frac { 25 } { 4 }\)
• B) \(y = - \frac { 4 } { 3 } x + \frac { 25 } { 3 }\)
• C) \(y = - \frac { 3 } { 4 } x + \frac { 25 } { 4 }\)
• D) \(y = \frac { 3 } { 4 } x - 25\)
• E) \(y = - \frac { 3 } { 4 } x + 25\)

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Definitions:

Natural Monopoly

A type of monopoly that exists due to the high cost or complexity of operating in a specific industry, which effectively prevents other competitors.

Monopoly Inefficiency

The loss of economic efficiency that occurs when a single firm controls the market, leading to higher prices and lower product quantity or quality than in competitive markets.

Perfect Price Discrimination

A market strategy where a seller charges each buyer their maximum willingness to pay, capturing the entire consumer surplus as profit.

Willingness-to-Pay

The maximum amount a consumer is prepared to spend on a good or service.