Write a Polar Equation In $r$ And $\theta$ Of an Ellipse with the Focus at the Origin, with Ellipse

question 22

Multiple Choice

Write a polar equation in $r$ and $\theta$ of an ellipse with the focus at the origin, with the eccentricity $0.8$ and vertex at $\left( 1 , \frac { \pi } { 2 } \right)$ .

• A) \(r = \frac { 1.8 } { 1 - 4 \cos \theta }\)
• B) \(r = \frac { 9 } { 1 + 4 \sin \theta }\)
• C) \(r = \frac { 1.8 } { 5 - 4 \cos \theta }\)
• D) \(r = \frac { 9 } { 5 + 4 \sin \theta }\)
• E) \(r = \frac { 9 } { 5 - 4 \cos \theta }\)

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Definitions:

Proportions

The relationship between parts and a whole, often expressed as a ratio or fraction.

Factor 1

An element or component that contributes to a particular result or situation; can be considered as a contributing variable in different contexts.

Profit

The financial gain obtained when the revenue from selling goods or services exceeds the costs involved in their production or provision.

Production Function

A production function is an equation that describes the maximum output of a good or service an economy or firm can produce given the input resources it has available.