Which Set of Parametric Equations Represents the Following Line or Conic

question 70

Multiple Choice

Which set of parametric equations represents the following line or conic?
Use $x = h + a \sec \theta$ and $y = k + b \tan \theta$ .
Hyperbola: vertices $( - 10 , - 1 ) , ( 2 , - 1 )$
foci $( - 11 , - 1 ) , ( 3 , - 1 )$

• A)
• \(\begin{array} { l }
• x = 4 + \sqrt { 13 } \sec \theta \\
• y = 1 + 6 \tan \theta
• \end{array}\)
• B)
• \(\begin{array} { l }
• x = - 4 + \sqrt { 13 } \sec \theta \\
• y = - 1 + 6 \tan \theta
• \end{array}\)
• C)
• \(\begin{array} { l }
• x = - 1 + \sqrt { 13 } \sec \theta \\
• y = - 4 + 6 \tan \theta
• \end{array}\)
• D)
• \(x = - 4 + 6 \sec \theta\)
• \(y = - 1 + \sqrt { 13 } \tan \theta\)
• E)
• \(\begin{array} { l }
• x = - 1 + 6 \sec \theta \\
• y = - 4 + \sqrt { 13 } \tan \theta
• \end{array}\)

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Definitions:

Acting Out

Acting out is the expression of emotional conflict or feelings through actions, often inappropriate or disruptive, as a substitute for verbal expression.

Humanistic

An approach in psychology that emphasizes empathy and stresses the good in human behavior.

Hypotheses

Proposed explanations or predictions for specific phenomena, typically based on limited evidence, to be tested through further investigation.

Tentative Explanations

Preliminary hypotheses or guesses made to explain a phenomenon, subject to further confirmation or refutation.