Question

What conic is represented by 2x2 + xy + 3y2 – 3x + 4y - 1 = 0? Show your work.

Answer 1

Explanation:

For a conic section in the form of

`a {x}^(2) + bxy + {cy}^(2) + dx + ey + f = 0`

If

`{b}^(2) - 4ac = 0`

Then the conic section is a parabola

If

`{b}^(2) - 4ac > 0`

Then the conic section is a hyperbola,

If

`{b}^(2) - 4ac < 0`

We have two cases:

If a=c, then the conic is a circle

If not, then the conic is a ellipse

Here, b is 1, a is 2, and c is 3

So

`{1}^(2) - 4(2)(3) = 1 - 24 = - 23`

Since the discriminant is less than 0, and a is not equal to c, this conic is an ellispe.