Identifying Conic Sections

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 parabola that opens to the right?

Back

The standard form is (y - k)² = 4p(x - h), where (h, k) is the vertex and p is the distance from the vertex to the focus.

Front

How do you identify a circle from its equation?

Back

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

Front

What is the definition of an ellipse?

Back

An ellipse is a set of points where the sum of the distances from two fixed points (foci) is constant.

Front

What is the standard form of a horizontal ellipse?

Back

The standard form 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

What is the relationship between the foci and vertices of a hyperbola?

Back

In a hyperbola, the distance between the foci is greater than the distance between the vertices.

Front

What is the equation of a hyperbola that opens horizontally?

Back

The standard form is (x - h)²/a² - (y - k)²/b² = 1, where (h, k) is the center.

Front

How do you find the value of b² for a hyperbola?

Back

For a hyperbola, b² can be found using the relationship c² = a² + b², where c is the distance from the center to the foci.

Front

What is the focus of a parabola?

Back

The focus of a parabola is a fixed point located along the axis of symmetry, where all points on the parabola are equidistant from the focus and the directrix.

Front

What is the directrix of a parabola?

Back

The directrix of a parabola is a line perpendicular to the axis of symmetry, used to define the parabola along with the focus.