Conic Sections

Front

What is a conic section?

Back

A conic section is a curve obtained by intersecting a cone with a plane. The four types of conic sections are circles, ellipses, parabolas, and hyperbolas.

Front

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

Back

Front

What is the standard form of an ellipse's equation?

Back

Front

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

Back

Front

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

Back

Front

What is the focus of a parabola?

Back

The focus of a parabola is a fixed point located along the axis of symmetry, where all points on the parabola are equidistant from the focus and the directrix.

Front

What is the directrix of a parabola?

Back

The directrix of a parabola is a fixed line perpendicular to the axis of symmetry, such that any point on the parabola is equidistant from the focus and the directrix.

Front

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

Back

Front

What is the relationship between the axes of symmetry and the conic sections?

Back

The axes of symmetry are lines that divide the conic sections into two mirror-image halves. For circles and ellipses, there are two axes; for parabolas, there is one; and for hyperbolas, there are two.

Front

What is the difference between a major axis and a minor axis in an ellipse?

Back

The major axis is the longest diameter of the ellipse, passing through the foci, while the minor axis is the shortest diameter, perpendicular to the major axis.