[Prelim] Pre-Calculus

Question 1

Parts of Conic Section:

Answer 1

• Axis
• Generator
• Vertex

Question 2

Types of Conic Sections:

Answer 2

• Circle
• Parabola
• Ellipse
• Hyperbola

Question 3

Degenerate Conic Sections:

Answer 3

• Point
• Single Line
• Pair of interseating Lines

Question 4

Two millennia ago, Apollonius of Perga, the great Greek geometer,studied the curves formed by the intersection of a plane and a double right circular cone(double-napped circular cone),and discovered many properties of these curves. These curves were later known as ___________.

Answer 4

Conic Sections

Question 5

Two millennia ago, ___________, the great Greek geometer,studied the curves formed by the intersection of a plane and a double right circular cone(double-napped circular cone),and discovered many properties of these curves. These curves were later known as conic sections.

Answer 5

Apollonius of Perga

Question 6

A line perpendicular to the base of the double right circular cone.

Answer 6

Axis

Question 7

A line lying entirely on the cone.

Answer 7

Generator

Question 8

Point of intersection of the two cones.

Answer 8

Vertex

Question 9

Are curves formed by the intersection of a plane and a double-napped circular cone.

Answer 9

Conic Section

Question 10

The plane is perpendicular to the axis.

Answer 10

Circle

Question 11

The plane intersects only one cone; parallel to only one generator.

Answer 11

Parabola

Question 12

The plane is not perpendicular to the axis and is not parallel to any generator or is oblique to the cone’s axis.

Answer 12

Ellipse

Question 13

The plane cuts both halves of the cone or intersects both cones and is parallel to two generators.

Answer 13

Hyperbola

Question 14

Plane cuts the double right circular cone through the vertex only(degenerate ellipse/circle).

Answer 14

Point

Question 15

The cutting plane is parallel to one generator and passes through the vertex.(degenerate parabola)

Answer 15

Single Line

Question 16

The cutting plane is parallel to two generators, cut both halves of the cone,and passes through the vertex.(degenerate hyperbola)

Answer 16

Pair of intersecting lines

Question 17

A simple evaluation of an expression called _____________ can easily provide information on the type of conic section.

Answer 17

Discriminant

Question 18

The _______ is the distance from the center outwards.

Answer 18

Radius

Question 19

The _________ goes straight across the circle, through the center.

Answer 19

Diameter

Question 20

The ____________ is the distance once around the circle.

Answer 20

Circumference

Question 21

Is the shortest word and shortest measure.

Answer 21

Radius

Question 22

Is longer

Answer 22

Diameter

Question 23

Is longest

Answer 23

Circumference

Question 24

A line that “just touches” the circle as it passes by is called a ______.

Answer 24

Tangent

Question 25

A line that cuts the circle at two points is called a _______.

Answer 25

Secant

Question 26

A line segment that goes from one point to another on the circle’s circumference is called a _____.

Answer 26

Chord

Question 27

If it passes through the center it is called a _________.

Answer 27

Diameter

Question 28

A part of the circumference is called an ______.

Answer 28

Arc

Question 29

Quarter of a circle is called a _______.

Answer 29

Quadrant

Question 30

Half a circle is called a _________.

Answer 30

Semicircle

Question 31

A set of coplanar points such that the distance from a fixed point is constant.- A set of equidistant points.

Answer 31

Circle

Question 32

A line segment whose endpoints are on a circle.

Answer 32

Chord

Question 33

Twice the size of the radius; cuts the circle into two equal parts, passing through the center.

Answer 33

Diameter

Question 34

A line or plane that touches a curve or other plane at exactly one point (Point of Tangency).

Answer 34

Tangent

Question 35

A line that intersects a circle in two points.

Answer 35

Secant

Question 36

Having the same center.

Answer 36

Concentirc

Question 37

Used to solve for the distance between points

Answer 37

Distance Formula

Question 38

Gives you the coordinates of the center point of a segment.

Answer 38

Midpoint Formula

Question 39

Terms of circle:

Answer 39

• Chord
• Diameter
• Tangent
• Secant
• Concentric