Conic Sections: Parabolas, Ellipse, & Circle

Front

What is a parabola?

Back

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

Front

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

Back

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

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 that is perpendicular to the axis of symmetry of the parabola, and every point on the parabola is equidistant from the focus and the directrix.

Front

How do you determine the direction a parabola opens?

Back

If the coefficient 'a' in the standard form y = a(x - h)² + k is positive, the parabola opens upwards; if 'a' is negative, it opens downwards.

Front

What is the vertex of a parabola?

Back

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

Front

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

Back

The standard form 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

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

Back

The standard form 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

What is an ellipse?

Back

An ellipse is a closed curve that results from the intersection of a cone with a plane that is inclined to the axis of the cone, where the sum of the distances from any point on the ellipse to two fixed points (foci) is constant.

Front

What is the standard form of an ellipse?

Back

The standard form is (x - h)²/a² + (y - k)²/b² = 1, where (h, k) is the center, a is the semi-major axis, and b is the semi-minor axis.