Conics Review

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 an ellipse?

Back

Front

What are the foci of an ellipse?

Back

Front

What is the equation of a hyperbola?

Back

Front

What are the vertices of an ellipse?

Back

The vertices of an ellipse are the endpoints of the major axis. For a vertical ellipse, they are at (h, k±a), and for a horizontal ellipse, they are at (h±a, k).

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, while the minor axis is the shortest diameter, perpendicular to the major axis.

Front

How do you find the co-vertices of an ellipse?

Back

The co-vertices of an ellipse are located at (h±b, k) for a horizontal ellipse and (h, k±b) for a vertical ellipse, where b is the semi-minor axis.

Front

What is the relationship between the axes of a hyperbola?

Back

In a hyperbola, the transverse axis is the line segment that connects the vertices, while the conjugate axis is perpendicular to the transverse axis at the center.

Front

What is the standard form of a circle?

Back

Front

How do you convert the general form of a conic to standard form?

Back

To convert the general form of a conic to standard form, complete the square for the x and y terms and rearrange the equation.