00:01
In this question, you're asked to identify the conic section for the equation 3x squared plus 6xy minus y squared plus 6x with 4.
00:08
The way to solve for this problem is by solving for the equation b squared minus 4ac, which i've written in the blue.
00:16
And basically, if this equation is equal to 0, then it's a parabola.
00:20
If it's greater than 0, it's a hyperbola, and if it's less than 0, it's an ellipse.
00:24
And the way to solve for b squared minus 4ac is by finding out what b and c are equal.
00:31
By comparing the red and black equations.
00:35
And so first, you have 3x squared in the black equation, and in the right equation you have an ax squared.
00:43
And since x squared's coefficient is a in the red equation, and x squared's coefficient is 3 in the black equation, that means that a is equal to 3.
00:56
Then you have a plus 6xy and a plus bxy in the right equation...