Question

How to tell the difference between hyperbolas parabolas and ellipses and circles?

Answer 1

Explanation:

The general form of a conic section:

Ax^2+Bxy+Cy^2+Dx+Ey+F=0

If B = 0, then:

Ellipse: x² and y² have different positive coefficients.

Hyperbola: x² and y² have different signs.

Otherwise, determine the discriminant:

If B² − 4AC < 0, then the conic is an ellipse.

If B² − 4AC > 0, then the conic is a hyperbola.

Answer 2

Different difintions:
A circle is the set of all points in a plane that are equidistant from a given point called the centre of the circle.
An ellipse is the set of all poins in a plane such that sum of the distances from two fixed points (foci) is constant.
A parabola the set of all points in a plane equidistant from a fixed point (focus) and a fixed line (directrix).
A hyperbola is the set of all points in a plane such that the difference of the distances from two fixed points (foci) is constant.