(HAA) Conics: Parabolas (including review) 2024

Front

What is a parabola?

Back

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

Front

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

Back

The standard form 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 focus of a parabola?

Back

The focus is a fixed point located inside the parabola, where all the reflected rays converge.

Front

What is the directrix of a parabola?

Back

The directrix is a fixed line used in the definition of a parabola, which is perpendicular to the axis of symmetry.

Front

How do you find the vertex of a parabola given its equation in standard form?

Back

For the equation (x-h)² = 4p(y-k), the vertex is at the point (h,k).

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

What is the relationship between the focus and directrix in a parabola?

Back

The distance from any point on the parabola to the focus is equal to the distance from that point to the directrix.

Front

What is the equation of a parabola that opens to the right?

Back

The standard form is (y-k)² = 4p(x-h), where (h,k) is the vertex.

Front

How do you determine the width of a parabolic arch at a given height?

Back

Use the vertex form of the parabola and substitute the height into the equation to find the corresponding width.

Front

What is the significance of the value 'p' in the parabola's equation?

Back

The value 'p' represents the distance from the vertex to the focus and also from the vertex to the directrix.