Use a Table of Values to Graph the Plane Curve $x = 2 \tan t , y = 5 \sec t$

question 240

Multiple Choice

Use a table of values to graph the plane curve defined by the following parametric equations. Find a rectangular
equation for the curve.
- $x = 2 \tan t , y = 5 \sec t$ , for $t$ in $[ 0,2 \pi ]$

• A) \(y = 5 \sqrt { 1 + \frac { x ^ { 2 } } { 4 } }\), for \(x\) in \(( - \infty , \infty )\)
• B) \(\frac { y ^ { 2 } } { 25 } + \frac { x ^ { 2 } } { 4 } = 1\), for \(x\) in \(( - \infty , \infty )\)
• C) \(\frac { y ^ { 2 } } { 25 } - \frac { x ^ { 2 } } { 4 } = 1\), for \(x\) in \(( - \infty , \infty )\)
• D) \(y = x ^ { 2 } - 9\), for \(x\) in \([ - 3,3 ]\)

---

Definitions:

Index Variable

Utilized in programming constructs to navigate through elements in data structures like arrays by incrementing or decrementing its value.

Loop Terminates

Loop termination occurs when a loop's continuation condition has ceased to be true, signaling the end of the loop's execution.

Insertion Sort

A simple sorting algorithm that builds the final sorted array one item at a time by repeatedly inserting a new element into the correct position.

Sorting Phase

The sorting phase is part of an algorithm or process where data elements are arranged in a specified order, such as ascending or descending.