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A hyperbola is centered at C = (3,7).  The vertices are (9,7) and (-3,7).  The slopes...

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kristenmarieb... | Student, Grade 10 | Valedictorian

Posted July 2, 2013 at 10:13 PM via web

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A hyperbola is centered at C = (3,7).  The vertices are (9,7) and (-3,7).  The slopes of the asymptotes are m = + or - 5/6.  

Enter the equation of the hyperbola in the form:

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

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mvcdc | Student , Undergraduate | (Level 1) Associate Educator

Posted July 2, 2013 at 10:24 PM (Answer #1)

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Notice that the center and vertices have the same y-coordinate. This means that they lie on the same horizontal line, and the hyperbola's branches lie side by side (not above and below) each other - i.e. we have a parabola of the first form (of your equations above).

Hence, the slope of the asympotes are given by: `pm b/a.`

This gives us `b=5` and `a=6.`

The center gives us h and k. In this case, `h = 3` and `k = 7`.` `

Hence, our hyperbola is given by the following equation:

`((x - 3)^2)/36 - ((y - 7)^2)/25 = 1`

 

 

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