# SOLUTION: what is the equation of a hyperbola with vertex (6,4) and (6,8) and foci(6,0 and 6,12. i really need an answer for this quickly so any help would be appreciated:-)

Algebra ->  Algebra  -> Quadratic-relations-and-conic-sections -> SOLUTION: what is the equation of a hyperbola with vertex (6,4) and (6,8) and foci(6,0 and 6,12. i really need an answer for this quickly so any help would be appreciated:-)      Log On

 Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help! Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations!

 Algebra: Conic sections - ellipse, parabola, hyperbola Solvers Lessons Answers archive Quiz In Depth

 Click here to see ALL problems on Quadratic-relations-and-conic-sections Question 18281: what is the equation of a hyperbola with vertex (6,4) and (6,8) and foci(6,0 and 6,12. i really need an answer for this quickly so any help would be appreciated:-)Answer by khwang(438)   (Show Source): You can put this solution on YOUR website! what is the equation of a hyperbola with vertex (6,4) and (6,8) and foci(6,0) and (6,12). Mid point of (6,4) & (6,8) is (6,6) : center, and the principal axis is vertical. Assume the equation of the hyperbola is: Set x = 6, y = 4, we have , so (or use dist|(6,4),(6,12)| - dist|(6,4),(6,0)| = 4 = 2a to get a = 2) Since the distance between two foci (6,0) & (6,12) is 12 = 2c, so c = 6. by c^2 = a^2 + b^2 = 36,we have b^2 = 32. [Note e = c/a = 3] Therefore, the equation is Kenny