Conics Parabolas

Front

What is a parabola?

Back

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

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 does the value of 'p' represent in a parabola?

Back

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

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 determine the direction a parabola opens?

Back

If the coefficient of the squared term is positive, the parabola opens upwards; if negative, it opens downwards.

Front

What is the vertex of a parabola?

Back

The vertex is the highest or lowest point of the parabola, depending on its orientation.

Front

What is the axis of symmetry in a parabola?

Back

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

Front

How do you find the coordinates of the focus from the equation (y-k)² = 4p(x-h)?

Back

The focus is located at (h+p, k) for a right-opening parabola and (h-p, k) for a left-opening parabola.

Front

What is the relationship between the focus and the directrix?

Back

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