Writing Equations of Parabolas

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 (focus) and a fixed line (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 focus of a parabola?

Back

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

Front

What is the directrix of a parabola?

Back

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

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 value of p in a parabola?

Back

The value of p can be found by measuring the distance from the vertex to the focus or from the vertex to the directrix.

Front

Given the focus (3, 4) and vertex (3, 2), what is the equation of the parabola?

Back

(x-3)² = 8(y-2) because p = 2 (distance from vertex to focus).

Front

Given the directrix y = 1 and vertex (2, 2), what is the equation of the parabola?

Back

(x-2)² = 8(y-2) because p = 2 (distance from vertex to directrix).

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, passing through the vertex.