Conics

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 equation of a circle with center (h, k) and radius r?

Back

The standard equation of a circle is (x - h)² + (y - k)² = r².

Front

How do you identify a circle from its equation?

Back

A circle can be identified by the equation in the form (x - h)² + (y - k)² = r², where r is the radius.

Front

What is the difference between an ellipse and a circle?

Back

An ellipse is a stretched circle, defined by two focal points, while a circle has a constant radius from its center.

Front

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

Back

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

Front

What is a hyperbola?

Back

A hyperbola is a type of conic section formed by the intersection of a plane and a double cone, characterized by two separate curves.

Front

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

Back

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

Front

How do you determine if a hyperbola is vertical or horizontal?

Back

A hyperbola is horizontal if the x² term is positive and vertical if the y² term is positive in its standard equation.

Front

What are the foci of a conic section?

Back

Foci are fixed points used to define and construct conic sections. For ellipses, there are two foci; for hyperbolas, there are also two.

Front

What is the relationship between the lengths of a, b, and c in an ellipse?

Back

In an ellipse, the relationship is c² = a² - b², where c is the distance from the center to each focus.