Conics Review

Front

What is the center of a conic section?

Back

The center of a conic section is the point that serves as the midpoint of the conic's axes. For example, the center of a circle or an ellipse is the point from which all points on the conic are equidistant.

Front

What is a parabola?

Back

A parabola is a conic section that can be 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). It has only one squared term in its equation.

Front

How do you find the center of an ellipse?

Back

Front

What is the standard form of a hyperbola?

Back

Front

What distinguishes a vertical hyperbola from a horizontal hyperbola?

Back

A vertical hyperbola opens upwards and downwards, while a horizontal hyperbola opens left and right. This is determined by the placement of the squared terms in the standard form.

Front

What is the focus of a conic section?

Back

The focus of a conic section is a fixed point used in the definition of the conic. For ellipses and hyperbolas, there are two foci, while for parabolas, there is one.

Front

What is the directrix of a parabola?

Back

The directrix of a parabola is a fixed line used in its definition. Each point on the parabola is equidistant from the focus and the directrix.

Front

How do you determine if a conic is a circle?

Back

Front

What is the equation of a circle with center (2, -3) and radius 5?

Back

Front

What is the eccentricity of a conic section?

Back

Eccentricity is a measure of how much a conic section deviates from being circular. For circles, eccentricity is 0; for ellipses, it is between 0 and 1; for parabolas, it is 1; and for hyperbolas, it is greater than 1.