HPC Ch. 12 Parabolas (Conics)

Front

What is a parabola?

Back

A parabola is a U-shaped curve that is defined as the set of all points equidistant from a fixed point called the focus and a fixed line called the directrix.

Front

What is the vertex of a parabola?

Back

The vertex is the highest or lowest point on the parabola, depending on its orientation. It is the point where the parabola changes direction.

Front

What is the directrix of a parabola?

Back

The directrix is a fixed line used in the definition of a parabola. It is perpendicular to the axis of symmetry and is located opposite the focus.

Front

What is the axis of symmetry in a parabola?

Back

The axis of symmetry is a vertical or horizontal line that divides the parabola into two mirror-image halves.

Front

How do you determine the direction a parabola opens?

Back

The direction a parabola opens can be determined by the sign of the coefficient in the quadratic equation: positive opens up or right, negative opens down or left.

Front

What is the standard form of a vertical parabola?

Back

The standard form of a vertical parabola is (x-h)² = 4p(y-k), where (h,k) is the vertex and p is the distance from the vertex to the focus.

Front

What is the standard form of a horizontal parabola?

Back

The standard form of a horizontal parabola is (y-k)² = 4p(x-h), where (h,k) is the vertex and p is the distance from the vertex to the focus.

Front

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

Back

To find the focus, identify the vertex from the equation and use the value of p to determine the focus's position relative to the vertex.

Front

What is the focal width of a parabola?

Back

The focal width is the distance between the points on the parabola that are parallel to the directrix and pass through the focus.

Front

What is the relationship between the directrix and the focus?

Back

The directrix and the focus are equidistant from any point on the parabola.