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 a circle's equation?

Back

The standard form of a circle's equation is (x - h)² + (y - k)² = r², where (h, k) is the center and r is the radius.

Front

What defines a parabola?

Back

A parabola is 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).

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.

Front

What is the difference between a vertical and horizontal hyperbola?

Back

A vertical hyperbola opens upwards and downwards, with the standard form (y - k)²/a² - (x - h)²/b² = 1. A horizontal hyperbola opens left and right, with the form (x - h)²/a² - (y - k)²/b² = 1.

Front

What is the standard form of an ellipse?

Back

The standard form of an ellipse 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.

Front

How do you find the center of a circle from its equation?

Back

The center of a circle can be found from the equation (x - h)² + (y - k)² = r², where (h, k) are the coordinates of the center.

Front

What is the relationship between the axes of an ellipse?

Back

In an ellipse, the length of the major axis is greater than the length of the minor axis. The semi-major axis (a) is half the length of the major axis, and the semi-minor axis (b) is half the length of the minor axis.

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.

Front

What is the directrix of a parabola?

Back

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