[Prelim] Xy Calculus

Question 1

Curves formed by the intersection of a plane and a double napped circular cone

Answer 1

CONIC SECTIONS

Question 2

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

Answer 2

AXIS

Question 3

A line lying entirely on the cone.

Answer 3

GENERATOR

Question 4

Point of intersection of the two cones.

Answer 4

VERTEX

Question 5

The plane is perpendicular to the axis.

Answer 5

CIRCLE

Question 6

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

Answer 6

PARABOLA

Question 7

• Formed when the plane is not perpendicular to the axis and is not parallel to any generator or is oblique to the cone’s axis
• Slightly tilted

Answer 7

Ellipse

Question 8

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

Answer 8

Hyperbola

Question 9

• Plane cuts the double right circular cone through the vertex only
• degenerate ellipse / circle

Answer 9

Point

Question 10

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

Answer 10

Single Line

Question 11

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

Answer 11

PAIR OF INTERSECTING LINES

Question 12

It’s a _______________ if it passes through the vortex

Answer 12

Degenerate Conic

Question 13

• A simple evaluation of an expression
• easily provide information on the type of conic section

Answer 13

DISCRIMINANT

Question 14

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

Answer 14

Circles

Question 15

Fixed point on a circle

Answer 15

Center

Question 16

Distance from the center to any point on the circle

Answer 16

Radius

Question 17

• A line segment whose endpoints are on a circle.
• You know where it ends

Answer 17

Chord

Question 18

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

Answer 18

Diameter

Question 19

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

Answer 19

Tangent

Question 20

• A line that intersects a circle in two points
• Infinite length

Answer 20

Secant

Question 21

Having the same center

Answer 21

Concentric

Question 22

Standard form:

Answer 22

(𝑥−h)2+ (𝑦−𝑘)2 = 𝑟2

Question 23

General Form:

Answer 23

𝐴𝑥2+𝐶𝑦2+𝐷𝑥+𝐸𝑦 = 0

Question 24

Used to solve for the distance between points

Answer 24

Distance Formula

Question 25

Gives you the coordinates of the center point of a segment

Answer 25

Midpoint formula

Question 26

Parts of the conic section:

Answer 26

Axis Generator Vertex

Question 27

Types of conic sections:

Answer 27

Circle Parabola Ellipse Hyperbola

Question 28

Degenerate conic section:

Answer 28

Point Single line Pair of intersecting lines

Question 29

Terms/part of circle:

Answer 29

Chord Diameter Tangent Secant Concentric