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Which Set of Parametric Equations Represents the Following Line or Conic

Question 17

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 (5,3) ,(11,3) \quad ( 5 , - 3 ) , ( 11 , - 3 )
foci (0,3) ,(16,3) ( 0 , - 3 ) , ( 16 , - 3 )


A)
x=8+55secθy=3+3tanθ\begin{array} { l } x = - 8 + \sqrt { 55 } \sec \theta \\y = 3 + 3 \tan \theta\end{array}
B)
x=8+55secθy=3+3tanθ\begin{array} { l } x = 8 + \sqrt { 55 } \sec \theta \\y = - 3 + 3 \tan \theta\end{array}
C)
x=3+55secθy=8+3tanθ\begin{array} { l } x = - 3 + \sqrt { 55 } \sec \theta \\y = 8 + 3 \tan \theta\end{array}
D)
x=8+3secθy=3+55tanθ\begin{array} { l } x = 8 + 3 \sec \theta \\y = - 3 + \sqrt { 55 } \tan \theta\end{array}
E)
x=3+3secθy=8+55tanθ\begin{array} { l } x = - 3 + 3 \sec \theta \\y = 8 + \sqrt { 55 } \tan \theta\end{array}

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