A conic section or conic is the locus of a point P that moves in such a way that its distance from a fixed point S always bears a common ratio to its distance from a fixed line, all being in the same plane.

**Focus**

The fixed point S is called the focus of the conic section.

**Directrix**

The fixed straight line is called the directrix of the conic section.

**Eccentricity**

The constant ratio is called the eccentricity of the conic section and is generally denoted by e.

- If e = 0 the conic is a circle
- If e < 1 the conic is an ellipse
- If e = 1 the conic is a parabola
- If e > 1 the conic is a hyperbola

**Axis**

The straight line passing through the focus and perpendicular to the directrix is called the axis of the conic section.

**Vertex**

The points of intersection of the conic section and the axis are called the vertices of the conic section.

**Center**

The point that bisects every chord passing through it is called the center of the conic section.

**Latus Rectum**

The latus rectum of a conic is the chord passing through the focus and perpendicular to the axis.

Let S = (h, k) be the focus

Ax + By + C = 0 be the directrix

e = eccentricity

of the conic.

Let P( x1, y1) be any point on the conic.

Let PM be the perpendicular from P on the directrix. Then, by definition

Collecting like terms together,

is also called the discriminant.

Consider the following equations. State which equation is a circle, parabola, ellipsis and hyperbola.

**i) Solutions**

**ii) Solutions**

**iii) Solutions**

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