Conic Sections

These flashcards cover key vocabulary and concepts related to Conic Sections, detailing definitions and properties of various shapes like circles, ellipses, hyperbolas, and parabolas.

Conic Section

The curves that can be obtained by cutting a cone with a plane.

Circle

A set of points such that the distance of each point from a fixed point (center) remains constant.

Ellipse

A set of points such that the sum of the distances from any point on it to two fixed points (foci) is constant.

Hyperbola

A set of points such that the difference of the distances from any point on it to two fixed points (foci) is constant.

Parabola

A set of points in a plane equidistant from a fixed point (focus) and a fixed straight line (directrix).

Vertex

The common intersection point of all the cone's elements.

Focus (F)

A fixed point used in the definition of a parabola, ellipse, and hyperbola.

Directrix

A fixed straight line used in the definition of a parabola.

Radius

The constant distance from the center to any point on the circle.

Tangent

A straight line that touches the curve at a point without cutting the curve.

Normal

A straight line perpendicular to the curve at the point of tangency.

Latus Rectum

A focal chord of the parabola that is perpendicular to the axis of the parabola.

Eccentricity (e)

A measure of how much a conic section deviates from being circular.

Asymptotes

Lines that a hyperbola approaches but never touches.

Parametric Equations

Equations that express the coordinates of the points of a curve as functions of a variable called a parameter.

Translation of Axis

A transformation that shifts the origin of the coordinate system.

Rotation of Axis

A transformation that changes the orientation of the coordinate axes.

Locus

A set of points that satisfy a given condition.