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Which Set of Parametric Equations Represents the Following Line or Conic

Question 118

Multiple Choice

Which set of parametric equations represents the following line or conic?
Use x=h+asecθx = h + a \sec \theta and y=k+btanθy = k + b \tan \theta .
Hyperbola: vertices (5,7) ,(3,7) ( - 5,7 ) , ( - 3,7 )
foci (8,7) ,(0,7) ( - 8,7 ) , ( 0,7 )


A)
x=4+15secθy=7+tanθ\begin{array} { l } x = 4 + \sqrt { 15 } \sec \theta \\y = - 7 + \tan \theta\end{array}
B)
x=4+15secθy=7+tanθ\begin{array} { l } x = - 4 + \sqrt { 15 } \sec \theta \\y = 7 + \tan \theta\end{array}
C)
x=7+15secθy=4+tanθ\begin{array} { l } x = 7 + \sqrt { 15 } \sec \theta \\y = - 4 + \tan \theta\end{array}
D)
x=4+secθx = - 4 + \sec \theta
y=7+15tanθy = 7 + \sqrt { 15 } \tan \theta
E)
x=7+secθy=4+15tanθ\begin{array} { l } x = 7 + \sec \theta \\y = - 4 + \sqrt { 15 } \tan \theta\end{array}

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