Focus and Directrix Day 1

Front

What is a parabola?

Back

A parabola is a symmetrical, U-shaped curve that is defined as the set of all points that are equidistant from a fixed point (the focus) and a fixed line (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 that is perpendicular to the axis of symmetry and is used in the definition of the parabola.

Front

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

Back

The equation can be derived using the distance formula, setting the distance from any point on the parabola to the focus equal to the distance from that point to the directrix.

Tags

CCSS.HSG.GPE.A.2

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

If a parabola opens upwards, what can you say about its focus and directrix?

Back

The focus is above the vertex, and the directrix is below the vertex.

Front

If a parabola opens downwards, what can you say about its focus and directrix?

Back

The focus is below the vertex, and the directrix is above the vertex.

Front

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

Back

For any point on the parabola, the distance to the focus is equal to the distance to the directrix.

Front

How do you determine the equation of the directrix given the focus?

Back

For a vertical parabola, if the focus is at (0,p), the directrix is at y = -p. For a horizontal parabola, if the focus is at (p,0), the directrix is at x = -p.