Mathematics Lecture on Conic Sections and Sequences

Flashcards summarizing key vocabulary and concepts from the lecture on conic sections and sequences.

Hyperbola

A conic section created by intersecting a plane with a double napped cone, characterized by two foci and the absolute difference of distances from the foci being constant.

Eccentricity (e)

A measure of how much a conic section deviates from being circular, defined as the ratio of the distance from a point on the conic to a focus and the distance from the point to the directrix.

Latus Rectum

A line segment perpendicular to the axis of a conic that passes through a focus.

Standard Equation of a Circle

x² + y² = r², represents a circle with center at the origin and radius r.

Conic Section

The intersection of a plane with a double-napped cone, resulting in shapes like circles, ellipses, parabolas, and hyperbolas.

Directrix

A line that, along with a focus, helps define the conic sections.

Vertex

The point on the axis of a conic where it intersects the axis.

Principal Axis

The axis that passes through the center and foci of a conic section.

Arithmetic Sequence

A sequence of numbers in which the difference between consecutive terms is constant.

Geometric Sequence

A sequence where each term after the first is obtained by multiplying the previous term by a fixed, non-zero number.

Series

The sum of terms in a sequence.

Focus (Foci)

Points about which the conic section is created.

Chord of Contact

A line segment that connects the points of contact of tangents drawn from an external point to a conic section.

Vertical Ellipse

An ellipse that opens vertically, with the major axis along the y-axis.

Horizontal Ellipse

An ellipse that opens horizontally, with the major axis along the x-axis.

Parabola

A conic section defined by a quadratic equation, which has one focus and a directrix.

Infinity in Series

Indicates an infinite series in mathematical notation.

Arithmetic Mean

The average of a set of numbers, often used in the context of sequences.