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21 votes
21 votes
In the hyperbola, 4x^2 − 9y^2 = 36, the focci are located at:a. (±6,0)b. (0,±6c. (±√13, 0)d. (0, ±√13)e. (0,0)

User Karan K
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1 Answer

12 votes
12 votes

Since the equation of the hyperbola is


4x^2-9y^2=36

Divide all terms by 36


\begin{gathered} (4x^2)/(36)-(9y^2)/(36)=(36)/(36) \\ (x^2)/(9)-(y^2)/(4)=1 \end{gathered}

Since the form of the equation of the hyperbola is


(x^2)/(a^2)-(y^2)/(b^2)=1

By comparing them


\begin{gathered} a^2=9 \\ b^2=4 \end{gathered}

Since the foci are (c, 0) and (-c, 0)

Since the value of c can be found from the rule


c^2=a^2+b^2

Then


\begin{gathered} c^2=9+4 \\ c^2=13 \end{gathered}

Find the square root of both sides


c=\pm\sqrt[]{13}

The foci are


(\sqrt[]{13},0),(-\sqrt[]{13},0)

Then the answer is C

User Shikjohari
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