Use the following definition. The line segment that has...

Use the following definition. The line segment that has endpoints on a parabola, passes through the focus of the parabola, and is perpendicular to the axis of symmetry is called the latus rectum of the parabola.
Find the latus rectum for the parabola given by $y^{2}=-4 x$.

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Key Concepts

Parabola

A parabola is a conic section defined as the set of all points equidistant from a fixed point (the focus) and a fixed line (the directrix). Its characteristic U-shaped curve exhibits symmetry about a central line.

Focus of a Parabola

The focus is a critical point in a parabola's definition from which distances to any point on the parabola are equal to the distances from that point to the directrix. The location of the focus determines the parabola’s shape and orientation.

Latus Rectum

The latus rectum of a parabola is a line segment that passes through the focus, is perpendicular to the axis of symmetry, and has both endpoints on the parabola. Its length provides a measure of the parabola’s width at the focus and is crucial in analyzing the parabola’s geometric properties.

Axis of Symmetry

The axis of symmetry is an imaginary line that divides the parabola into two mirror-image halves. It passes through the vertex and the focus, serving as a central line around which the geometry of the parabola is organized.

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