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 also be defined as the set of all points equidistant from a fixed point (focus) and a fixed line (directrix).

Front

What are the key components of a parabola?

Back

The key components of a parabola include the vertex, focus, directrix, and axis of symmetry.

Front

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

Back

The equation of a parabola can be determined using the distance formula, where the distance from any point on the parabola to the focus equals the distance from that point to the directrix.

Front

What is the vertex of a parabola?

Back

The vertex of a parabola is the point where it changes direction, and it is located midway between the focus and the directrix.

Front

What is the focus of a parabola?

Back

The focus of a parabola is a fixed point located inside the curve, which is used to define the parabola.

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.

Front

How does the value of 'p' affect the shape of a parabola?

Back

The value of 'p' represents the distance from the vertex to the focus (and to the directrix). A larger 'p' value results in a wider parabola, while a smaller 'p' value results in a narrower parabola.

Front

What is the standard form of a vertical parabola?

Back

The standard form of a vertical parabola is given by the equation y = a(x - h)² + k, where (h, k) is the vertex.

Front

What is the standard form of a horizontal parabola?

Back

The standard form of a horizontal parabola is given by the equation x = a(y - k)² + h, where (h, k) is the vertex.

Front

How do you find the coordinates of the focus from the equation of a parabola?

Back

For a parabola in the form y = a(x - h)² + k, the focus is located at (h, k + 1/(4a)). For a horizontal parabola x = a(y - k)² + h, the focus is at (h + 1/(4a), k).