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I pick that a=6

Ok, answer me, pick a , b such that 9 = a^2 -b^2

9 = 6^2 -b^2

9 = 36- b^2

a =6 , hence a^2 =36, so b =?

b^2 = 27 but b = 5.196

ok, how about a =5 and b=4? do they work?

Your pick is PERFECTLY ok. I just suggest the easiest numbers to work with.

If a = 5 and b = 4, it would be the following:
25-16=9

Yes, hence your ellipse equation will be??? just plug into the standard form for HORIZONTAL one.

http://www.math.binghamton.edu/grads/kaminski/math222_spring12/Sect10.5_ShiftedConics.pdf

Print it out to use later. It is helpful

Look at Horizontal Ellipse row. the formula right on the 3rd column.

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