PRE-CAL TERMS M7-11

Parabola circle ellipse hyperbola

4 Basic tyoe of conics

1. Add/Subtract 2. Substitution 3. Graphing

3 Common Methods in solving systems of equations in 2 unknowns

parabola - The line is called the directrix, and the point is called the focus.

A _____ is the set of all points equidistant from a line and a fixed point not on the line.

circle - point is called center, distance from center to any point is called radius

A _____ is the set of all points on a plane that are equidistant from a fixed point on the plane.

right triangle

A _______ is a three-sided polygon with a right angle.

right circular cone.

A conic is the intersection of a plane and a

difference

A hyperbola is the set of points in a plane such that the _____ of the distances of each point of the set from two fixed points (foci) in the plane is constant.

line

A is a one-dimensional figure, which has length but no width.

opposite directions

A line is made up of a set of points which is extended in ________ infinitely. It is determined by two points in a two-dimensional plane.

one and only one

A system of three linear equations in three unknowns usually has ________ solution.

standard positions

An angle is said to be in _______ if its vertex coincides with the origin in the rectangular system and one ray (the initial side) lies on the positive - axis while the other ray (terminal side) lies on any of the quadrant.

oblique

An ________ triangle is one that does not contain a right angle.

ellipse

An _______is the set of all points P in a plane such that the sum of the distances of P from two fixed points on the plane is constant.

geometric shapes

Analytic geometry is concerned with defining and representing ___________ in a numerical way.

Simultaneous Equations

Applications of mathematics lead to more that one equation in several variables results to?

properties of space.

Geometry is a branch of mathematics that is concerned with the shapes and sizes of the objects, their relative position, and the ________

Euclidean

Geometry which deals with the study of plane and solid figures.

three

Every triangle has _____ vertices and three sides.

Quadrantal angle.

If the terminal side of an angle lies on the x-axes such as 0, 90, 180 degress, it is called a ?

True

If there are two distinct points, then there is only one and only one straight line that can be drawn through both points. T or F

coterminal angles.

If two angles in standard position have the same terminal side, they are called _____________.

square bracket

In the case of a matrix, the value is enclosed in a ______

Hyperbola

It is an open curve with two branches, the intersection of a plane with both halves of a double cone.

Analytic Geometry

It is the foundation of most modern fields of geometry, including algebraic, differential, discrete and computational geometry.

parallel, negative reciprocals

Lines are ____________ if the slopes are equal and lines are perpendicular if their slopes are ____________.

elimination method

The addition/subtraction is also known as?

terminal side

The angle is measured by the amount of rotation from the initial side to the ________

augmented matrix.

Matrices can be used to solve systems of equations. A system of equations can be represented by an __________

focal chord.

The chord that passes through the focus of a parabola, cutting the parabola at two distinct points is called the

major axis

The chord through a focus and perpendicular to the _________ is called a latus rectum.

center of the hyperbola.

The midpoint of the line joining the two foci is called the _________

True

The minor axis is the shortest diameter (at the narrowest part of the ellipse). T or F

Inconsistent or dependent

Sometimes, however, such a system may have no solution, in which case the equations are called __________, or infinitely many solutions which are called _______.

intersection

The _____ of the axes of the ellipse is the center.

midpoint of a segment

The _________ is the point on the segment that is equidistant from the endpoints.

point-slope form

The _________ of the equation of a line requires a point on the line and the slope of the line.

reference angle

The acute angle between the terminal side and the x - axis is called the________ which is always less than 90degrees and always positive.

two vertical lines

The determinant of a matrix is represented by _______ or simply by writing det and writing the matrix name.

scalar value

The determinant of a matrix is the ______ or number calculated using a square matrix. The square matrix could be 2x2, 3x3, 4x4, or any type, such as n x n, where the number of column and the rows are equal.

vertices

The ends of the major axis are called the _______.

conic section

The graph of a second-degree equation in the coordinates x and y is called a

algebraic equations.

The importance of analytic geometry is that it establishes a correspondence between geometric curves and _________

sum of the squares

The law of cosines states that the square of a side of a triangle is equal to the ___________ of the other two sides minus twice the product of the two sides and the cosine of the included angle.

side length

The law of sines is defined as the ratio of the _______ to the sine of the opposite angle.

axis

The line containing the focus and the vertex is the ______ of the parabola, and the parabola is symmetric with respect to its axis.

conjugate axis

The line passing through the center of the hyperbola and perpendicular to the transverse axis is called the ________ of the hyperbola.

transverse axis

The line passing through the two foci and the center of the hyperbola is called the ________ of the hyperbola.

True - It goes from one side of the ellipse, passing through the center, to the other side, at the widest part of the ellipse.

The major axis is the longest diameter. T or F

counterclockwise

The measurement is positive if it is measured in a __________ direction.

bounding sides

The perimeter (P) of a closed plane figure is the sum of the lengths of its _______ (line segment or arcs).

vertex.

The point on the parabola halfway between the focus and the directrix is the

hypotenuse

The side opposite the right angle is called the

all solutions

The solution set of a system of equations consists of __________ that are common to the equations in the system.

Pythagorean Theorem

The sum of the squares of the perpendicular sides of a right triangle is equal to the square of the hypotenuse.

T

The value of a trigonometric function of a real number t is its value at an angle of t radians, provided that value exists. T or F

space

The volume of a solid is the measure of how much _______ an object takes up. It is measured in cubic units.

latus rectum

The_________ is the focal chord that is perpendicular to the axis of the parabola and is passing through the focus of the parabola.

area (A)

The____of a closed figure is the region of the plane enclosed by the figure's boundary.

Euclidean

There are three types of geometry, namely, _________, Hyperbolic, and Elliptical.

Substitution Method

This method involves substituting one equation into the other.

Minor of an Entry

To evaluate the determinant of a 3 x 3 matrix, evaluate the ______ in the determinant.

Analytic Geometry

_______ which is also known as coordinate geometry or Cartesian geometry is the study of geometry using a coordinate system.

Matrix

a rectangular arrangement of numbers into rows and columns.

Cramer's Rule

is a method of solving systems of equations using determinants.

Parametric equation

is a type of equation that employs an independent variable called a parameter (often denoted by t) and in which dependent variables are defined as continuous functions of the parameters and are not dependent on another existing variable.

2 point form

is an expansion of the point-slope form of the equation of the line.

legs

the perpendicular sides are called the_____ of the right triangle.