Algebra conics

Conics

What is the general center point of a conic section?

- The center is represented as (h, k).

What is the vertex of a parabola in standard form? -

The vertex is at the point (h, k).

What is the equation for a parabola that opens upwards? -

The equation is y - k = (1/(4p))(x - h)².

What defines the focal length of a conic section? - The focal length is denoted as p.

- The focal length is denoted as p.

What is the relationship between a, b, and c in conic sections?

- c² = a² + b², where c is the distance from the center to the foci.

What are the lengths of the major and minor axes in an ellipse?

- The length of the major axis is 2a, and the length of the minor axis is 2b.

What is the equation for a hyperbola centered at (h, k)?

- The equation is (x-h)²/a² - (y-k)²/b² = 1 for a horizontal hyperbola.

What is the significance of negative coefficients in conic sections?

- Negative coefficients indicate a reflection or flip of the parabola.