Question

what is the conic section of
6x^2-12=30x-6y^2+y

Answer 1

\(\large {6x^2-12=30x-6y^2+y\implies
\begin{array}{llll}6x^2-12-30x&+6y^2-y=0\\
\uparrow &\uparrow \\
\textit{positive }x^2&\textit{positive }y^2
\end{array}}\)

so... ?

Answer 2

ellipse?

Answer 3

well, yes, if both "x" and "y" squared are the same sign, positive or negative, it'd be an ellipse

and if their coefficient is the same, like in this case, is a ROUND ellipse, otherwise known as a circle

Answer 4

then what about y^2-x^2-12x+12y -4=0 ? what would that one be? i have no idea:(

Answer 5

hmmm you just did one of those just before this one

Answer 6

when either squared "x" or "y" is negative, you'd have a hyperbola

Answer 7

omg thank you!!!

Answer 8

yw

Answer 9

@jdoe0001 I want to confirm: x, y both - / + --> ellipse
x, y different signs, --> hyperbola
how about circle?
It's new to me, I want to know, please

Answer 10

ohh same as an ellipse really, since a circle is just a round ellipse
but on a circle, the coefficients for "x" and "y" squared are the same
in an ellipse the coefficients differ

Answer 11

Thank you.