Trying to solve conic for ellipse equation

Question

I'm trying to find out what conic the following equation represents.

$9x^2+4y^2+18x-16y+24 = 0$

I know that the general ellipse equation is $(x^2)/a + (y^2)/b = 1.$

I got $9(x+1)^2 + 4(y-2)^2 = 1$, but I am not sure what to do next.

For example if I had some number instead of $1$, I could easily divide everything and get the "correct" equation pattern, but since I already have a $1$ on the right, I am not sure what to do.

Regards, L.K.

Your very first expression is missing an " = " somewhere and another number/expression in the other side of this symbol — DonAntonio, Dec 17 '13 at 12:28
Most probably you can't comment as you're still lacking reputation points, but you can edit your question and add the missing info. — DonAntonio, Dec 17 '13 at 12:34

score 1 · Accepted Answer · answered Dec 17 '13 at 12:30

1

If, for some reason, what you say you get is correct then

$$9(x+1)^2+4(y-2)^2=1\iff \frac{(x+1)^2}{\frac19}+\frac{(y-2)^2}{\frac14}=1\implies a=\frac13\;,\;b=\frac12$$

Remember that for any non-zero number $\;a\;$ , we have

$$a=\frac1{\frac1a}$$

answered Dec 17 '13 at 12:30

DonAntonio

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Sorry to bother you again, but didn't you mean (y-2)^2 instead of (y-2)^4 ? – Laury Dec 17 '13 at 12:34
Yes, of course: typo. Thanks. – DonAntonio Dec 17 '13 at 12:35

Trying to solve conic for ellipse equation

1 Answers1