Midterm Reviewer - Pre Calculus

Conic Section

Curves formed by the intersection of a plane with one or two nappes of a cone.

Non-degenerate Conics

Circle, parabola, ellipse, and hyperbola formed by the intersection of a plane with a cone.

Circle

A conic section formed when the plane is parallel to the base of the cone.

Parabola

A conic section formed when the plane intersects only one cone to form an unbounded curve.

Ellipse

A conic section formed when the tilted plane intersects only one cone to form a bounded curve.

Hyperbola

A conic section formed when the plane intersects both cones to form an unbounded curve.

Degenerate Conics

Conic sections resulting from a plane intersecting the double cone and passing through the apex.

Point

A degenerate conic section resulting from a plane intersecting the double cone at a single point.

Line

A degenerate conic section resulting from a plane intersecting the double cone in a straight line.

Two intersecting lines

A degenerate conic section resulting from a plane intersecting the double cone in two intersecting lines.

General Form of Non-degenerate Conics

The general form equation for a conic section, where A, B, and C are not all zero.

Circle Coefficient

A circle has A = C ≠ 0 in the general form equation.

Parabola Coefficient

A parabola has AC = 0 in the general form equation.

Ellipse Coefficient

An ellipse has AC > 0 in the general form equation.

Hyperbola Coefficient

A hyperbola has AC < 0 in the general form equation.

Circle

A set of all points in a plane equidistant from a fixed point called the center.

Arc

A portion of the circumference of a circle.

Chord

A line segment connecting two points on a circle.

Diameter

A chord that passes through the center of a circle.

Radius

The distance from the center of a circle to any point on its circumference.

Secant Line

A straight line that intersects a circle in two points.

Tangent Line

A line that touches a circle at a single point.

Sector

The region bounded by an arc of a circle and the two radii to the arc's endpoint.

Equations of a Circle

Equations for a circle with its center at the origin or at (h, k) and its radius r.

Parabola

The locus of all points in the plane whose distances from a fixed point and a fixed line are the same.

Focus

A fixed point on a parabola.

Directrix

A fixed line not passing through the focus of a parabola.

Axis of Symmetry

A line passing through the focus and perpendicular to the directrix of a parabola.

Latus Rectum

A line segment passing through the focus and perpendicular to the axis of symmetry of a parabola.

Equations of a Parabola

Equations for a parabola with its focus, directrix, and axis of symmetry.

Ellipse

The set of all points in a plane whose sum of distances from two specific points is a constant.

Foci

Two fixed points on an ellipse.

Center

The midpoint of the foci of an ellipse.

Major Axis

The longest diameter of an ellipse passing through the foci.

Minor Axis

The shortest diameter of an ellipse perpendicular to the major axis at the center.

Semi-major Axis

Half of the major axis of an ellipse.

Semi-minor Axis

Half of the minor axis of an ellipse.

Equations of Ellipse

Equations for an ellipse with its center at the origin or at (h, k).

Hyperbola

The set of all points in a plane whose distances from two fixed points have an absolute difference equal to a constant.

Branches

The separate curves that form a hyperbola.

Vertices

The points on the separate branches of a hyperbola where the distance is at a minimum.

Center

The midpoint between the vertices of a hyperbola.

Asymptotes

Lines that a hyperbola approaches as it heads towards infinity.

Transverse Axis

The line segment formed by the vertices of a hyperbola.

Conjugate Axis

The line segment perpendicular to the transverse axis through the center of a hyperbola.

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