Hyperbolas and parabolas

Front

What is a hyperbola?

Back

A hyperbola is a type of conic section that appears as two separate curves, defined by the difference of distances from two fixed points (foci) being constant.

Front

What is a parabola?

Back

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

Front

What is the standard form of a hyperbola's equation?

Back

The standard form of a hyperbola's equation is (y²/a²) - (x²/b²) = 1 or (x²/a²) - (y²/b²) = 1.

Front

What is the standard form of a parabola's equation?

Back

The standard form of a parabola's equation is y = a(x - h)² + k, where (h, k) is the vertex.

Front

What are the foci of a hyperbola?

Back

The foci of a hyperbola are the two fixed points located along the transverse axis, used to define the hyperbola.

Front

What is the directrix of a parabola?

Back

The directrix of a parabola is a line that is perpendicular to the axis of symmetry and is used in the definition of the parabola.

Front

How do you find the vertices of a hyperbola?

Back

The vertices of a hyperbola are found at (±a, 0) for horizontal hyperbolas and (0, ±a) for vertical hyperbolas, where 'a' is the distance from the center to the vertices.

Front

What is the relationship between the foci and vertices of a hyperbola?

Back

The distance from the center to the foci (c) is greater than the distance from the center to the vertices (a), where c² = a² + b².

Front

What is the axis of symmetry for a parabola?

Back

The axis of symmetry for a parabola is a vertical or horizontal line that passes through the vertex and divides the parabola into two mirror-image halves.

Front

What is the difference between a hyperbola and an ellipse?

Back

A hyperbola consists of two separate curves, while an ellipse is a closed curve. The difference in distances from the foci is constant for hyperbolas, while the sum of distances is constant for ellipses.