Find a Rectangular Equation for the Plane Curve Defined by the Parametric

question 110

Multiple Choice

Find a rectangular equation for the plane curve defined by the parametric equations.
- $$x = 3 \tan t , y = 2 \sec t ; 0 \leq t \leq 2 \pi$$

• A) \(y = x ^ { 2 } - 9\); for \(x\) in \(- 3 \leq x \leq 3\)
• B) \(y = 3 \sqrt { 1 + \frac { x ^ { 2 } } { 25 } }\); for \(x\) in \(- \infty < x < \infty\)
• C) \(\frac { y ^ { 2 } } { 9 } - \frac { x ^ { 2 } } { 25 } = 1\); for \(x\) in \(- \infty < x < \infty\)
• D) \(\frac { y ^ { 2 } } { 9 } + \frac { x ^ { 2 } } { 25 } = 1\); for \(x\) in \(- \infty < x < \infty\)

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Definitions:

Hasty Generalization

A logical fallacy where a conclusion is reached on the basis of insufficient evidence, generalizing too quickly from too little information.

Composition

The fallacy of inferring that a whole has a property merely because its parts have that property.

Division

A fallacy where one assumes that what is true of a whole must also be true of its parts.

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