SOLUTION: Dear sir/Ma'am, Please help me with this math problem: center(1,-2), transverse axis parallel to the x-axis, transverse axis= 6, conjugate axis = 10. Find the equation of th

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Question 812914: Dear sir/Ma'am,
Please help me with this math problem:
center(1,-2), transverse axis parallel to the x-axis, transverse axis= 6, conjugate axis = 10. Find the equation of the hyperbola.
Thank you so much!

Answer by jsmallt9(3758)   (Show Source): You can put this solution on YOUR website!
The standard forms for equations of ellipses are:
for horizontally-oriented hyperbolas and
for vertically-oriented hyperbolas
Since the transverse axis is parallel to the x-axis in this problem, this hyperbola is horizontally-oriented. So we will be using the first form.

In both forms, the coordinates of the center are represented by the 'h' and the 'k'. So with a center of (1, -2) out 'h' is 1 and our 'k' is -2.

In both forms the 'a' represents the distance from the center to a vertex on the transverse axis. Since the center is halfway between the two vertices on the transverse axis, 'a' is 1/2 of the length of the transverse axis. This makes our 'a' 1/2 of 6 or, more simply, 3.

With similar logic the 'b' is 1/2 the length of the conjugate axis. So our 'b' is 1/2 of 10 or just 5.

With our 'h', 'k', 'a' and 'b' we are now ready to write the equation. Inserting the values we have found into we get:

which simplifies to:

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