True or False? In Exercises 103-108 , determine whether the...

True or False? In Exercises $103-108$ , determine whether the statement is true or false. Justify your answer.
The directrix of the parabola $x^{2}=y$ intersects, or is tangent to, the graph of the parabola at its vertex, $(0,0)$ .

Key Concepts

Tangent

A tangent line is one that touches a curve at exactly one point without crossing it at that point. In the context of conic sections such as parabolas, a tangent can have special properties, particularly at the vertex, where it might align with or just touch a significant component of the parabola. This concept is essential when exploring the interactions between curves and lines in analytical geometry.

Vertex

The vertex of a parabola is the point where the curve changes direction and is often considered the 'turning point' of the parabola. It is equidistant from both the focus and the directrix, serving as a natural midpoint in the parabola's geometry. Analyzing the vertex is crucial when studying the intersections and tangency of lines with the parabola.

Directrix

The directrix of a parabola is the fixed line used in the definition of the curve. Every point on the parabola is equidistant from the directrix and the focus, which makes the directrix a fundamental tool in deriving the equation of a parabola. It plays a critical role in understanding the geometric properties and behavior of the parabola, including how it interacts with lines such as tangents.

Parabola

A parabola is a type of conic section defined as the set of all points that are equidistant from a fixed point called the focus and a fixed line known as the directrix. This geometric definition leads to a symmetric curve that opens either upward, downward, or to the side, depending on its orientation. Understanding the parabola helps in studying its different components such as its vertex and axis of symmetry.

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