Parabolas and Hyperbolas Flashcard

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 (the focus) and a fixed line (the directrix).

Front

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

Back

Front

What is the focus of a parabola?

Back

The focus is a fixed point located inside the parabola, which is used to define the curve.

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

Front

What is the axis of symmetry of a parabola?

Back

The axis of symmetry is a vertical line that passes through the vertex of the parabola, dividing it into two mirror-image halves.

Front

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

Back

Front

What is a hyperbola?

Back

A hyperbola is a type of conic section that consists of two separate curves called branches, defined as the set of all points where the difference of the distances to two fixed points (foci) is constant.

Front

What is the center of a hyperbola?

Back

The center is the midpoint between the two foci of the hyperbola and is the point from which the hyperbola is symmetric.

Front

What is the standard form of a hyperbola?

Back