Focus and Directrix of a Parabola Flashcard

Front

What is the definition of a parabola?

Back

A parabola is a symmetric curve formed by the intersection of a cone with a plane parallel to its side. It can be defined as the set of all points equidistant from a fixed point (the focus) and a fixed line (the directrix).

Front

What is the focus of a parabola?

Back

The focus of a parabola is a fixed point located inside the curve, where all the reflected rays converge. It is used to define the parabola's shape.

Front

What is the directrix of a parabola?

Back

The directrix of a parabola is a fixed line used in conjunction with the focus to define the parabola. Any point on the parabola is equidistant from the focus and the directrix.

Front

What is the vertex of a parabola?

Back

The vertex of a parabola is the point where the parabola changes direction. It is the midpoint between the focus and the directrix.

Front

What is the standard form equation of a parabola that opens upwards or downwards?

Back

Front

What is the standard form equation of a parabola that opens sideways?

Back

Front

How do you find the equation of a parabola given the focus and directrix?

Back

To find the equation, use the definition of a parabola: set the distance from any point (x, y) on the parabola to the focus equal to the distance to the directrix.

Front

What is the orientation of a parabola with a focus at (p, q) and a directrix of the form y = k?

Back

If the focus is above the directrix, the parabola opens upwards. If the focus is below, it opens downwards.

Front

What is the orientation of a parabola with a focus at (p, q) and a directrix of the form x = k?

Back

If the focus is to the right of the directrix, the parabola opens to the right. If the focus is to the left, it opens to the left.

Front

Given a parabola with vertex at the origin and focus at (0, p), what is the equation of its directrix?

Back