HYPERBOLA

Definition 
 
A hyperbola is a curve where the distances of any point from:

• a fixed point (the focus), and
• a fixed straight line (the directrix) are always in the same ratio. 

This ratio is called the eccentricity, and for a hyperbola it is always greater than 1.
The hyperbola is an open curve (has no ends).
But that isn't the full story! Because a hyperbola is actually two separate curves in mirror image like this:

On the diagram you can see:

• a directrix and a focus (one on each side)
• an axis of symmetry (that goes through each focus, at right angles to the directrix)
• two vertices (where each curve makes its sharpest turn)

The "asymptotes" (shown on the diagram) are not part of the hyperbola, but show where the curve would go if continued indefinitely in each of the four directions.
And, strictly speaking, there is also another axis of symmetry that reflects the two separate curves of the hyperbola.

Conic Section You can also get a hyperbola when you slice through a cone. The slice must be steeper than that for a parabola, but does not have to be parallel to the cone's axis for the hyperbola to be symmetrical. So the hyperbola is a conic section (a section of a cone).

Equation

By placing a hyperbola on an x-y graph (centered over the x-axis and y-axis), the equation of the curve is:

x²/a² − y²/b² = 1

Also: One vertex is at (a, 0), and the other is at (−a, 0) The asymptotes are the straight lines: y = (b/a)x y = −(b/a)x And the equation is also similar to the equation of the ellipse: x2/a2 + y2/b2 = 1, except for a "−" instead of a "+")

Eccentricity

We already mentioned the eccentricity (usually shown as the letter e), it shows how "uncurvy" (varying from being a circle) the hyperbola is.

On this diagram:

• P is a point on the curve,
• F is the focus and
• N is the point on the directrix so that PN is perpendicular to the directrix.

The ratio PF/PN is the eccentricity of the hyperbola (for a hyperbola the eccentricity is always greater than 1).
It can also given by the formula:

e =

Using "a" and "b" from the diagram above.


Latus Rectum

The Latus Rectum is the line through the focus and parallel to the directrix. The length of the Latus Rectum is 2b2/a.

REFERENCES
http://www.mathsisfun.com/geometry/hyperbola.html

Antonym, Sinonym, and Hiponym

Synonyms

Synonyms are words that have the same or very similar meaning. All words can have a synonym. Nouns, verbs, adjectives, adverbs and prepositions can have a synonym as long as both words are the same part of speech.

Examples of Synonyms

Adjectives: beautiful, lovely, gorgeous, stunning, striking

Nouns: House, home, dwelling, residence, abode, quarters

Verbs: jump, bound, leap, hop, skip

Prepositions: in, inside, within

  

Antonyms

Antonyms are words that have opposite meanings. For example, the antonym of long is short. Often words will have more than one antonym but as with synonyms it depends on the context. For instance, the word warm could have the antonym cool or chilly. In order to choose the correct antonym, you have to look at all the meanings and how the word is used. Cool can mean stylish as well as chilly so the word cool may not be the best choice.

Types of Antonyms

1.      Graded antonyms are word pairs that have variations between the two opposites. For example, big and little are antonyms but there are a lot of changes before you get to the opposite meaning. Like this:

Big, huge, bulky, full-size, slight, petite, little Other examples are:

a.       Sane and crazy

b.      Rich and poor

c.       Cool and hot

d.      Wet and dry

e.       Late and early

f.       Ignorant and educated

2.      Relational antonyms are pairs that have a relationship. Each word wouldn’t exist without the other. There can’t be a parent without a child or it’s either all or nothing. Other examples include:

a.       Servant and master

b.      Borrow and lend

c.       Come and go

d.      Toward and away

e.       Divisor and dividen 

 

Hypernim and Hyponym

Hypernym is A linguistic term for a word whose meaning includes the meanings of other words. in other word. Meanwhile hyponym is In linguistics, a specific term used to designate a member of a class. In other word hypernyms are general words and hyponyms are subdivisions of more general words.  it means, It describes what happens when we say 'An X is a kind of Y'—An eagle is a kind of bird, or simply, An eagle is a bird."
examples :

1.      Fish (hypernym) = lion fish, nemo, cichilds (hyponym)

2.      Color (hypernym)= red, white, black, pink (hyponym)

3.      Vegetable (hypernym)= watercress, lettuce, broccoli, green bean (hyponym)

4.      Fruit (hypernym) = orange, apple, watermelon, grape (hyponym)

            5.      Subject lesson (hypernym) = mathematic, English, chemistry, physic

METAPHOR

what is metaphor?

   A metaphor is a figure of speech that refers to something as being the same as another thing for rhetorical effect.a word or phrase for one thing that is used to refer to another thing in order to show or suggest that they are similar.an object, activity, or idea that is used as a symbol of something else.

Common Speech Examples of Metaphors

examples :

• My brother was boiling mad. (This implies he was too angry.)
• The assignment was a breeze. (This implies that the assignment was not difficult.)
• It is going to be clear skies from now on. (This implies that clear skies are not a threat and life is going to be without hardships)
• The skies of his future began to darken. (Darkness is a threat; therefore, this implies that the coming times are going to be hard for him.)
• Her voice is music to his ears. (This implies that her voice makes him feel happy)

Literary Metaphor

   Metaphors are used in all type of literature but not often to the degree they are used in poetry because poems are meant to communicate complex images and feelings to the readers and metaphors often state the comparisons most emotively. Here are some examples of metaphor from famous poem

Examples:   She is all states, and all princes, I.”

      John Donne, a metaphysical poet, was well-known for his abundant use of metaphors throughout his poetical works. In his well-known work “The Sun Rising,” the speaker scolds the sun for waking him and his beloved. Among the most evocative metaphors in literature, he explains “she is all states, and all princes, I.” This line demonstrates the speaker’s belief that he and his beloved are richer than all states, kingdoms, and rulers in the entire world because of the love that they share.

The metaphor category also contains these specialised types:

• Allegory: An extended metaphor wherein a story illustrates an important attribute of the subject.
• Catachresis: A mixed metaphor used by design and accident (a rhetorical fault).
• Parable: An extended metaphor narrated as an anecdote illustrating and teaching such as in aesop'a fables, or Jesus' teaching method as told in the bible.
• Pun: Similar to a metaphor, a pun alludes to another term. However the main difference is that a pun is a frivolous allusion between two different things whereas a metaphor is a purposeful allusion between two different things.

reference

https://en.wikipedia.org/wiki/Metaphor

http://literarydevices.net/metaphor/