PRECAL TERMS Ellipse and Hyperbola

Q2 parts of ellipse and hyperbola

It is defined as a locus of points such that the difference of the distances from any point of the curve to the fixed points is constant.

Hyperbola

Center (C)

It is the point in the middle of the hyperbola. This is where the two axes and the asymptotic line of hyperbola intersects.

Vertex (V)

It is the main point of the hyperbola. There are two vertices in this curve. This point is located nearer to the center of the curve than to the foci.

Foci (F)

These are the points located inside of the hyperbola. The foci are located next to the vertices.

Transverse Axis

It is the line that joining the two vertices and passes through the center and foci. This is the counter part of the major axis in the ellipse and it length measures as 2a.

Conjugate Axis

This is a shorter line that connects the points b_1, and b_2. It also passes through the center of the hyperbola.

Directrix Lines

These are the lines that is drawn in between of the curves of the hyperbola and parallel to the curves.

Asymptote Lines

These are the two lines that intersect the center of the hyperbola and they are asymptotic to the two curves.

Latera Recta

These are chords that pass through the foci.

Ellipse

Formed by a locus of points whose sum of the distance from the two fixed points is constant (2a).

Hyperbola

composed of pairs of parabolas whose openings are in opposite directions, and its shape is dependent on the value of eccentricity, which is always greater than one (> 1).

Ellipse

Eccentricity is BETWEEN 0 - 1

Center

It is the midpoint inside of the ellipse curve and denated by the symbol C.

Vertices

Are the main points of the curve expressed by the symbols V.

Foci

Are the fixed points of the Ellipse and it is the plural form of Focus. This point is located between the center and the vertices. They are represented by the symbol F1 and F2.

Directrix lines / also called directrices.

These are the lines which are located outside of the ellipse.

Minor Axis

It divides the curve into two symmetrical parts. The end points of this axis are called intercepts. The length of the minor axis is 2b.

Principal Axis / Major Axis

Another symmetrical axis in the ellipse but always longer in length compare to minor axis. The endpoints of the Principal or major axis are the vertices. The length of this axis is 2a.

Focal Distance

It is the distance between the one of the focus to the Center. It is denoted by the symbol c.

Latera Recta! plural form is latus rectum

it is the plural form of the latus rectum. The length of is (2b^2)/a

Eccentricity

is the ratio of the distances from the fixed point to the point P and from point P to the directrix line. The value can be obtained from the formula of c/a