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Question 566563: X^2-10x+37+4y^2+16y=0
I need the following:
Center
foci
Major axis
Minor Axis
I get stuck due to -8 issue
I a stuck
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
Your -8 issue is a self-inflicted wound. Properly done, -8 never appears anywhere in this problem. Also, take care how you type your expressions in the future: X and x are NOT the same thing, so technically you have a three variable equation. Just sayin'
First complete the squares:
Constants on the right!
Divide the 1st order  term coefficient by 2, square the result, add the new constant to both sides: -10 divided by 2 is -5, -5 squared is 25.
Factor a 4 out of both  terms:
\ =\ -37\ +\ 25)
4 divided by 2 is 2. 2 squared is 4. 4 inside the parentheses, 16 outside.
\ =\ -37\ +\ 25\ +\ 16)
Factor the two perfect square trinomials and collect terms in the RHS:
^2\ +\ 4(y\ +\ 2)^2\ =\ 4)
Divide through by the RHS constant so that the RHS becomes 1:
^2}{4}\ +\ \frac{(y\ +\ 2)^2}{1}\ =\ 1)
Compare to the equation of an ellipse centered at ) , axes parallel to the coordinate axes, major axis measuring  , minor axis measuring  , and foci at a distance of  from the center on the major axis.
^2}{a^2}\ +\ \frac{(y\ -\ k)^2}{b^2}\ =\ 1)
So your center is at ) . Foci at ) and ) . Major axis measures 4. Minor axis measures 2.
John
My calculator said it, I believe it, that settles it
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