Parabola

Conics-Parabola

Parabola

The locus of a point which moves so that its distance from a fixed point is equal to its distance from a fixed straight line.

Focus

A fixed point from which distances are measured for the construction of a parabola.

Directrix

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

Latus Rectum

The line segment that passes through the focus and is perpendicular to the axis of symmetry of the parabola.

Vertex

The point where the parabola changes direction, located at a specific distance from the focus and directrix.

Chord

A line segment joining two points on the curve of the parabola.

Slope of the Axis

The slope formed by the line connecting the focus and the vertex of the parabola.

Normal

A line perpendicular to the tangent at a given point on the parabola.

Equation of the Tangent

A linear equation that describes the tangent line to a parabola at a specific point.

Focal Chord

A chord that passes through the focus of the parabola.

Parameters (a, t)

Constants used in the parametric equations of a parabola to define its shape and orientation.

Centroid of Triangle

The point where three medians intersect, significant for triangles formed by co-normal points on a parabola.

Polar of a Point

The polar line of point (x1, y1) with respect to a parabola represents all tangents from that point to the parabola.

Orthocenter

The point where the altitudes of a triangle meet, in relation to tangents at three points on a parabola.

Semi Latus Rectum

Refers to half of the length of the latus rectum, related to focal chords.