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.

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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).