Analytical Geometry -CIRCLES

Analytical Geometry -CIRCLES

Click the below link:

https://youtu.be/hMn41wPapi8?si=EelCYwjsFT0q6OIv 

These Excel Shortcuts you should know, Step by step Explanation.

These Excel Shortcuts you should know, Step by step Explanation.

1. Ctrl + 1 - Format Cells

 2. Ctrl + T - Insert Table

 3. Ctrl + D - Fill Down from cell above

4. Ctrl + R - Fill Down from Cell Left

5. Ctrl + Page Up - Move One Sheet Left

 6. Ctrl + Page down - Move One Sheet Right

 7. Ctrl + Drag - Duplicate Worksheet

8. Ctrl + Shift + & - Add border outline

9. Ctrl + Shift + _ - Remove Borders

10. Tab - Accept function with Autocomplete

11. Alt + Enter - Start a New line in the same cell

12. Alt + F1 - Create chart on same worksheet

13. F11 - Create chart in new worksheet

14. F2 - Edit the Active Cell

15. F4 - Repeat Last Action

16. F7 - Open Spelling Check

17. Shift + F11 - New Worksheet

1.2 NEGATIVE FORMATION

 1.2 NEGATIVE FORMATION

What Is a Negative Sentence? – Meaning and Definition

A negative sentence is one that indicates that some action is not happening, something no longer exists or that a subject does not possess a particular quality. In most scenarios, it can be easily identified by the words ‘not’, ‘no’, ‘nobody’, ‘nothing’, ‘nowhere’ ‘no one’ and ‘none’ as well as some peculiar words have negative meaning like few, little, rarely, seldom, scarcely used in sentences.

How to Form a Negative Sentence? – Different Ways and Points to Remember

Most often, a negative sentence is formed simply by the addition of ‘not’ to the verb in the sentence. It is also the easiest way to identify a negative sentence. Then again, there are other ways to form and identify negative sentences. 

Forming Negative Sentences by Adding ‘Not’

Conventionally, adding a ‘not’ to the verb indicates that an action is not taking place. Even in doing this, there are a few things you need to know.

When verb forms of ‘to be’ and ‘do’ are used as main verbs, the word ‘not’ can be added immediately after the verb.

For example:

v She is not a teacher.

v I do not like anything sweet.

When modal verbs such as can, could, will, would, shall, should, must, need, may, might, etc. are used in a sentence, the word ‘not’ should be placed after these verbs.

For example:

v I cannot help you with your homework as I would be late.

v You must not be brooding over this.

v Jannet should not have spoken to her parents like that.

v She may not find it difficult to complete this level.

Sentences denoting all other tenses will have one or more helping verbs and a main verb. In these cases, the word ‘not’ is added after the first helping verb followed by the main verb or the second helping verb and the main verb. In addition to this, also see to it that you do not alter the conjugated form of the main verb (present participle/past participle).

For example:

v Olivia is not eating anything though we have been trying to get her to do it for more than half a day. (Present Continuous Tense)

v He has not cut the call yet. (Present Perfect Tense)

v They have not been marking their attendance regularly. (Present Perfect Continuous Tense)

v It was not raining when we left. (Past Continuous Tense)

v The teacher had not told us what to do for our internal assessment. (Past Perfect Tense)

v The nurse found out that the patient had not been taking his medicines as per prescription. (Past Perfect Continuous Tense)

v Amit will not have what you require to finish your project. (Simple Future Tense)

v Raksesh, Rupesh and Ratheesh will not be participating in the International Science Fair. (Future Continuous Tense)

v The train will not have arrived when you reach the station. (Future Perfect Tense)

v The children will not have been doing the work properly. (Future Perfect Continuous Tense)

Using Contractions

We have already discussed that adding ‘not’ to the verb will form a negative sentence. In addition to this, you should also know that some verbs such as (is, was, have, etc.) can have contracted forms which can be used instead of ‘verb + not’. Go through the following examples to learn how contractions are used.

Verb + not	Contraction	Verb + not	Contraction
Is not	Isn’t	Was not	Wasn’t
Are not	Aren’t	Were not	Weren’t
Has not	Hasn’t	Have not	Haven’t
Had not	Hadn’t	Cannot	Can’t
Could not	Couldn’t	Should not	Shouldn’t
Must not	Mustn’t	Need not	Needn’t
Will not	Won’t	Would not	Wouldn’t

 

Forming Negative Sentences Using

‘No’, ‘Nothing’, ‘Nobody’, ‘None’, ‘Nowhere’

Words such as ‘no’, ‘nothing’, ‘nowhere’, ‘none’, ‘nobody’, ‘no one’ can also be used to form negative sentences. Also using ‘not’ along with the verb followed by words such as ‘any’, ‘anything’, ‘anywhere’, ‘anyone’ and ‘anybody’ will also do the trick. Take a look at the following examples to learn how this works.

Example 1:

v Everyone had gathered in the auditorium. (Affirmative sentence)

v No one had gathered in the auditorium. (Negative sentence)

Example 2:

v We had asked everybody for their opinion on the newly implemented policies. (Affirmative sentence)

v We had asked nobody for their opinion on the newly implemented policies. (Negative sentence)

(or)

v We had not asked anybody for their opinion on the newly implemented policies. (Negative sentence)

Example 3:

v All of us were present for the unfurling of the National Flag. (Affirmative sentence)

v None of us were present for the unfurling of the National Flag. (Negative sentence)

Example 4:

v Everything was falling into place. (Affirmative sentence)

v Nothing was falling into place. (Negative sentence)

Example 5:

v We could hear the new music album playing everywhere. (Affirmative sentence)

v We could hear the new music album playing nowhere. (Negative sentence)

(or)

v We could not hear the new music album playing anywhere. (Negative sentence)

Negating Interrogative Sentences

To form negative interrogative sentences, what you can do is either use ‘not’ after the subject or using the contraction of the verb in the beginning of the interrogative sentence. Here are a few examples that you can refer to.

Example 1:

v Have you not read ‘The Tale of Two Cities’?

v Haven’t you read ‘The Tale of Two Cities’? (Negative interrogative)

Example 2:

v Does she not teach Hindi anymore?

v Doesn’t she teach Hindi anymore? (Negative interrogative)

                                    Video reference in English and Tamil

ENGLISH

https://youtu.be/Jjnl4jGSY_4?si=vyJbd1Lr4VjyDmVC

 TAMIL

https://youtu.be/iINq1R0KJrM?si=AvIH7HzJoc655C0h

 

Finding the Equation of a Circle and Center and Radius

Equation Of A Circle

The standard equation of a circle is given by:

(x-h)2 + (y-k)2 = r2

Where (h,k) is the coordinates of center of the circle and r is the radius. 

Before deriving the equation of a circle, let us focus on what is a circle? A circle is a set of all points which are equally spaced from a fixed point in a plane. The fixed point is called the center of the circle. The distance between the center and any point on the circumference is called the radius of the circle. In this article, we are going to discuss what is an equation of a circle formula in standard form, and find the equation of a circle when the center is the origin and the center is not an origin with examples.

Real life applications of Analytical Geometry

 Application of Mathematics in Real Life

Definition

        The study of geometry using coordinate points is known as coordinate geometry (or analytic geometry). It is a portion of geometry in which the position of a point is determined by coordinates. A series of values called coordinates is used to show the exact location of a point in the coordinate plane.

It’s always better to understand how information benefits us in the real world. Let’s look at how the co-ordinate geometry can be applied in practice.

Coordinate geometry applications

A few examples of coordinate geometry applications are shown below.

• It’s used to figure out how far two points are apart.
• It is used to calculate the dividing line ratio in the m:n ratio.
• It is used to find the line’s midpoint.
• It’s used to figure out how big a triangle in the Cartesian plane is.
• It’s used in physics, GPS, maps, and a variety of other fields under various names. The underlying principle is the same in every situation: you choose an origin, assign a measure of unit distance, and define two or three directions, and bingo, you can now locate any point! After a couple more points are fixed, do a few extra amazing things.
• Even a computer monitor employs some basic coordinate geometry concepts. Complex curves, conics, and shapes can be mathematically specified using algebraic equations, which would be impossible to analyze using pure geometry.

Some of the detailed applications are shown below.

The Digital Use

The text file or PDF file is an example of coordinate plane usage. The words or graphics in these files are written or edited using coordinate geometry. A 2-dimensional coordinate (x, y) system is used to read any PDF file that comprises text and graphics. Coordinate geometry is also used by scanners and photocopying machines to generate a perfect copy of the original image.

Use in GPS

The Global Positioning System (GPS) is a satellite navigation system that delivers position and timing information in all weather circumstances.

Nature, which surrounds mankind, is the most essential example of geometry in everyday life. Different geometrical shapes and patterns can be found in leaves, flowers, stems, roots, bark, and so on if one looks closely. Geometry is also important in the human digestive system since it is organised like a tube within a tube. Tree leaves come in a variety of forms, sizes, and symmetries. Different geometrical shapes are found in different fruits and vegetables; for example, an orange is a sphere, and after peeling it, one can see how the individual slices make a perfect spherical shape.

Determining Latitude and Longitude

A coordinate framework is required for defining the precise location of a place in the actual world. To assign geographic locations, a particular coordinate system known as the geographical coordinate system is utilised. When weather forecasters watch storms in real life, they note the absolute position on a regular basis to see the storm’s route and try to anticipate the storm’s future path based in part on these discoveries.

Locating Air Transport

Coordinate geometry is used to manage and regulate air traffic. The coordinates of the flight are used to describe the aircraft’s current location. Even if an aircraft moves a tiny distance (up, down, forward, or backward), the system updates the coordinates of flight for every small change in its position.

Defining the location of any object

A coordinate system can be used to determine the position of any item from its starting point (known as the origin) to its current location.

For example, we can measure the distance between the watch and the television from the other side of the room. Allow a horizontal gap of 10 metre between the television and the corner, and a vertical distance of 5 metre between the watch and the ground. If the room is 5 metres wide, we can easily locate the watch’s coordinates and use the distance calculation to calculate its real distance.

Projection of Maps

Map Any 3D curved object can be projected onto a flat 2D surface via projection. This approach can be used to portray the curved surface of the earth on a flat map, for example. A unique sort of coordinate system known as a projected coordinate system is utilised for these purposes. These are primarily used to display maps on a computer screen.

Technology

Technology is the most widespread use of geometry in everyday life. Geometry is used in almost all basic principles in robotics, computers, and video games. Computer programmers can work because they have access to geometric principles at all times. Geometric computations aid in the production of sophisticated graphics in video games, which is how the virtual world of video games is generated. Raycasting is a shooting technique that uses a 2-D map to stimulate the 3-D environment of video games. Raycasting aids in processing speed by performing computations for the vertical lines on the screen.

Art

What exactly does art entail? The formation of figures and shapes, a fundamental comprehension of 2-D and 3-D, knowledge of spatial concepts, and the contribution of estimating, patterns, and measurement are all included in art. From the foregoing, it is clear that art and geometry have a close link. Geometrical forms such as the circle, triangle, square, mandala, and octagon are used to create shapes. Furthermore, the design and shape of frames have a significant impact on the content of paintings or sculptures. Not to mention that the principles of projective geometry are the foundation for most painting perspectives.

Conclusion

In this article, we have understood the application of coordinate geometry in our day-to-day life. We have discussed how coordinate geometry is useful in our life and have discussed various examples of coordinate geometry which will help us to visualise the concept and ultimately help in a deeper understanding of the topic.