Conic Classification

Front

What is a conic section?

Back

A conic section is a curve obtained by intersecting a cone with a plane. The type of conic section depends on the angle of the plane relative to the cone.

Front

Name the four types of conic sections.

Back

Circle, Ellipse, Parabola, Hyperbola.

Front

What defines a circle in terms of conic sections?

Back

A circle is a set of points in a plane that are equidistant from a fixed point called the center.

Front

What is an ellipse?

Back

An ellipse is a conic section formed when a plane intersects a cone at an angle that is less steep than the side of the cone, resulting in a closed curve.

Front

What is the standard equation of a circle?

Back

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

Front

What is the standard equation of an ellipse?

Back

The standard equation of an ellipse centered at (h, k) is (x - h)²/a² + (y - k)²/b² = 1, where a and b are the semi-major and semi-minor axes.

Front

What characterizes a hyperbola?

Back

A hyperbola is a conic section formed when a plane intersects both halves of a double cone, resulting in two separate curves.

Front

What is the standard equation of a hyperbola?

Back

The standard equation of a hyperbola centered at (h, k) is (x - h)²/a² - (y - k)²/b² = 1 or (y - k)²/b² - (x - h)²/a² = 1.

Front

What is a parabola?

Back

A parabola is a conic section that is formed when a plane is parallel to the side of a cone, resulting in a U-shaped curve.

Front

What is the standard equation of a parabola?

Back

The standard equation of a parabola that opens upwards is (x - h)² = 4p(y - k), where (h, k) is the vertex and p is the distance from the vertex to the focus.