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