Definitions
American Heritage® Dictionary of the English Language, Fourth Edition 1.n. A plane curve, especially:
2.n. A conic section whose plane is not parallel to the axis, base, or generatrix of the intersected cone. 3.n. The locus of points for which the sum of the distances from each point to two fixed points is equal. 4.n. Ellipsis.

Century Dictionary and Cyclopedia
1.n. In geometry, a plane curve such that the sums of the distances of each point in its periphery from two fixed points, the foci, are equal. It is a conic section (see conic) formed by the intersection of a cone by a plane which cuts obliquely the axis and the opposite sides of the cone. The ellipse is a conic which does not extend to infinity, and whose intersections with the line at infinity are imaginary. Every ellipse has a center, which is a point such that it bisects every chord passing through it. Such chords are called diameters of the ellipse. A pair of conjugate diameters bisect, each of them, all chords parallel to the other. The longest diameter is called the transverse axis, also the latus transversum; it passes through the foci. The shortest diameter is called the conjugate axis. The extremities of the transverse axis are called the vertices. (See conic, eccentricity, angle.) An ellipse may also be regarded as a flattened circle—that is, as a circle all the chords of which parallel to a given chord have been shortened in a fixed ratio by cutting off equal lengths from the two extremities. The two lines from the foci to any point of an ellipse make equal angles with the tangent at that point. To construct an ellipse, assume any line whatever, AB, to be what is called the latus rectum. At its extremity erect the perpendicular AD of any length, called the latus transversum (transverse axis). Connect BD, and complete the rectangle DABK. From any point L, on the line AD, erect the perpendicular LZ, cutting BK in Z and BD in H. Draw a line HG, completing the rectangle ALHG....

...Name: Ernest Ng
Class: 4G (23)
Date: 2-7-06
Mathematics ACE: Ellipse Areas
Before we embark on solving the problem, let us first explore the definition of ellipse.
[pic]
An ellipse is a curve that is the locus of all points in the plane the sum of whose distances [pic] and [pic] from two fixed points [pic] and [pic] (the foci) separated by a distance of [pic] is a given positive constant [pic]
[pic]
While [pic] is called the major axis, [pic] is the semi major axis, which is exactly half the distance across the ellipse. Similarly, the corresponding parameter [pic] is known as the semi minor axis.
Parallels drawn from the formula for the area of circle ([pic]) and formula for the area of an ellipse (A = [pic]ab)
Formula for the area of a circle:[pic] where [pic] is the area, and [pic] is the radius.
In the case of a circle, radius a represents the semi major axis while radius b represents the semi minor axis. One can thus find the area of the circle through the formula A = [pic]ab, where a is equal to b. Hence circle, in actual fact, is a unique case of ellipse.
Proving that the area of an ellipse is πab
Procedures to take (Theory)
1. We have to let an ellipse lie along the x-axis and find the equation of the ellipse curve.
2. Upon finding the equation of the...

...Conic Sections
Ellipses
In this study guide we will focus on graphing ellipses but be sure to read and understand
the definition in your text.
Equation of an Ellipse (standard form)
Area of an Ellipse
( x − h) 2 ( y − k ) 2
+
=1
a2
b2
with a horizontal axis that measures 2a units, vertical axis
measures 2b units, and (h, k) is the center.
The long axis of an ellipse is called the major axis and the short
axis is called the minor axis. These axes terminate at points that
we will call vertices. The vertices along the horizontal axis will be
( h ± a, k ) and the vertices along the vertical axes will be ( h, k ± b) .
These points, along with the center, will provide us with a method
to sketch an ellipse given standard form.
A = π ab
Graph
( x − 5) 2 ( y − 8) 2
+
=1
9
25
First plot the center.
Then use a = 3 and
plot a point 3 units to
the left and 3 units to
the right of the
center.
Use standard form to
identify a, b, and the
center (h, k).
Next, use b = 5 and
plot a point 5 units up
and 5 units down
from the center.
Label at least 4
points on the ellipse.
In this example the major axis is the vertical axis and the minor axis is the horizontal
axis. The major axis measures 2b = 10 units in length and the minor axis measures
2a = 6 units in length. There are no x- and y- intercepts in this example....

...Advertisement (ad)
Definition:
Paid, non-personal, public communication about causes, goods and services, ideas, organizations, people, and places, through means such as direct mail, telephone, print, radio, television, and internet. An integral part of marketing, advertisements are public notices designed to inform and motivate. Their objective is to change the thinking pattern (or buying behavior) of the recipient, so that he or she is persuaded to take the action desired by the advertiser. When aired on radio or television, an advertisement is called a commercial. According to the Canadian-US advertising pioneer, John E. Kennedy (1864-1928), an advertisement is "salesmanship in print."
Marketing mix
Main article: Marketing mix
The marketing mix has been the key concept to advertising. The marketing mix was suggested by Professor E. Jerome McCarthy in the 1960s. The marketing mix consists of four basic elements called the four P’s. Product is the first P representing the actual product. Price represents the process of determining the value of a product. Place represents the variables of getting the product to the consumer like distribution channels, market coverage and movement organization. The last P stands for Promotion which is the process of reaching the target market and convincing them to go out and buy the product.
Advertising theory
Hierarchy of effects model
It clarifies the objectives of an advertising campaign and for...

...certain abnormal mental or behavioral patterns. Insanity defines a “mental illness” of such a severe nature that a person cannot distinguish fantasy from reality, cannot conduct his or her affairs due to psychosis, or is subject to uncontrollable impulsive behavior. Insanity distinguishes from low intelligence or mental deficiency due to age or injury. Insanity may manifest as violations of societal norms, including a person becoming a danger to themselves or others, though not all such acts are considered insanity. In modern usage insanity is most commonly encountered as an informal unscientific term denoting mental instability, or in the narrow legal context of the insanity defense.
In the derivation of the word insanity lies its definition. In English, the word sane derives from the Latin adjective sanus meaning healthy. The word insanity was first used in the 1550s. Naturally the word insane means unhealthy. From Latin insanus meaning mad, insane, then comes the root of in meaning not, in Latin. The phrase mens sana in corpore sano is often translated to mean a healthy mind in a healthy body. In law, mens rea means having had criminal intent, or a guilty mind, when the act was committed.
From this perspective, insanity can be considered as poor health of the mind, not necessarily of the brain as an organ. Rather it refers to defective function of mental processes such as reasoning. Back in early history, individuals believed that insanity began...

...Critically analyse this assertion in light of the problems associated with the precise definition
The study of religion may be as old as humankind itself according to one author. Defining religion is difficult as there are many definitions as there are many authors. The word religion is the most difficult to define because of the lack of a universally accepted definition. Specifically the root meaning of the word religion can be traced to Latin. Relegare or religion means to bind oneself, emanating from the Latin religio, which is translated to re-read emphasising tradition passing from generation to generation. Douglas Davies says “some have simply described religion as a belief in spiritual beings.” (10). In the book The World Religion there is a suggestion of approaches for tackling the question of religion such as viewing it anthropologically, sociologically, through history, in a scholarly way, theologically and by reductionism. In this paper I will try and assess the definition of religion from aforementioned views and identify the problems of defining religion.
James Cox states that in their introductory textbook on religion the American scholars Hall, Pilgrim and Cavanagh identify four characteristic problems with traditional definitions of religion; these are: vagueness, narrowness, compartmentasation and prejudice (9). The authors argue that vagueness means there are so many...

...ELLIPSE
9. Given the following equation
9x2 + 4y2 = 36
a) Find the x and y intercepts of the graph of the equation.
b) Find the coordinates of the foci.
c) Find the length of the major and minor axes.
d) Sketch the graph of the equation.
Solution
a) We first write the given equation in standard form by dividing both sides of the equation by 36
9x2 / 36 + 4y2 / 36 = 1
x2 / 4 + y2 / 9 = 1
x2 / 22 + y2 / 32 = 1
We now identify the equation obtained with one of the standard equation in the review above and we can say that the given equation is that of an ellipse with a = 3 and b = 2 (NOTE: a >b) .
Set y = 0 in the equation obtained and find the x intercepts.
x2 / 22 = 1
Solve for x.
x2 = 22
x = ± 2
Set x = 0 in the equation obtained and find the y intercepts.
y2 / 32 = 1
Solve for y.
y2 = 32
y = ± 3
b) We need to find c first.
c2 = a2 - b2
a and b were found in part a).
c2 = 32 - 22
c2 = 5
Solve for c.
...

...There are four types of conic sections, circles, parabolas, ellipses, and hyperbolas. The first type of conic, and easiest to spot and solve, is the circle. The standard form for the circle is (x-h)^2 + (y-k)^2 = r^2. The x-axis and y-axis radius are the same, which makes sense because it is a circle, and from
In order to graph an ellipse in standard form, the center is first plotted (the (h, k)). Then, the x-radius is plotted on both sides of the center, and the y-radius is plotted both up and down. Finally, you connect the dots in an oval shape. Finally, the foci can be calculated in an ellipse. The foci is found in the following formula, a^2 b^2 = c^2. A is the radius of the major axis and b is the radius of the minor axis. Once this is found, plot the points along the major axis starting from the center and counting c amount both directions.
In order to determine if an equation is an ellipse, the following three criteria must be met. There must be an x^2 and a y^2 just like in a circle. However, the coefficients of the x^2 and y^2 must be different. Finally, the signs must be the same. For example, equation 4 is an ellipse. 49x^2 + 25y^2 +294x 50y 759 = 0 has an x^2 and a y^2. It also has different coefficients in front of them, and finally, both have the same sign! There you have it, an ellipse!HyperbolasBoy, now it is starting to get tough! But dont worry, hyperbolas are not much...

...
Ellipse Construction, ContinuedParallelogramThe parallelogram method of constructing ellipses inscribes the ellipse withinellipsesa parallelogram. You may use conjugate diameters or the major and minoraxes to formulate the parallelogram so long as the sides of the parallelogramare parallel to the diameters or axes.
step1ActionGiven the major and minor axes or the conjugate diameters AB andCD, draw a rectangle or parallelogram . Make sure all sides are parallel to their respective sides.
2Divide the distance between AO and AJ into the same number ofequal parts.
3Starting at the ends of the minor axis CD, lightly draw straight linesthrough each point. The lines intersect forming the circumferenceof the ellipse.
4Lightly sketch the outline of the ellipse. Darken the outline usingfrench curves.
To draw an ellipse by the parallelogram method, use this table;
Focus-Directrix orEccentricityMethod
Given :the distance offocusfrom the directrix and eccentricity
Example : Draw an ellipse if the distance of focus from the directrix is 70
mm and the eccentricity is 3/4.
1. Draw the directrix AB and
axis CC’
2. Mark F on CC’ such that
CF= 70 mm.
3. Divide CF into 7 equal
parts and mark V at the
3
parts and mark V at the
fourth division from C.
Now, e = FV/ CV = 3/4.
4. At V, erect a perpendicular
VB = VF. Join CB. Through
F, draw a line at 45°to meet...

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