Question

How do you classify the conic −6x2+4y2+2x+9=0?

Answer 1

Answer:

This is a hyperbola

Step-by-step explanation:

There is a formula for this.

But an easy was of remembering this is that if x^2 and y^2 have the same coefficients then it is a circle.

The above conic is therefore not a circle.

If only x OR y is raised to the power 2 then it is a parabola.

The above conic is therefore not a parabola.

If the x and y raised to the power 2 have same signs then the conic is an ellipse.

The above conic is therefore not an ellipse.

If the x and y raised to the power 2 have opposite signs then the conic is an hyperbola.

The above conic is therefore a hyperbola.