Question

What conic section does the equation `2x^2+4xy+6y^2+6x+2y=6` represent?

Answer 1

First locate the coefficients for the `x^2` term, `A`, and the `y^2` term, `C`.

`A=2`
`C=6`

Characteristics of an ellipse.

`A*C>0`
`A!=C`

`2*6>0` True
`2!=6` True

This is an ellipse .