Focus and Directrix

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 standard form of a vertical parabola?

Back

The standard form of a vertical parabola is given by the equation y = ax^2 + bx + c, where 'a' determines the direction and width of the parabola.

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 perpendicular to the axis of symmetry, which, along with the focus, helps define the parabola.

Front

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

Back

The vertex of a parabola in standard form y = ax^2 + bx + c can be found using the formula: Vertex (h, k) = (-b/(2a), f(-b/(2a))).

Front

What is the relationship between the focus and directrix of 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 upwards with vertex at the origin?

Back

The equation is x^2 = 4py, where 'p' is the distance from the vertex to the focus.

Front

What is the equation of a parabola that opens to the right with vertex at the origin?

Back

The equation is y^2 = 4px, where 'p' is the distance from the vertex to the focus.

Front

If a parabola has a focus at (0, p) and a directrix at y = -p, what is its equation?

Back

The equation of the parabola is x^2 = 4py.

Front

How do you determine the focus and directrix from the equation of a parabola?

Back

For the equation y^2 = 4px, the focus is at (p, 0) and the directrix is x = -p.