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Try typing or saying show me the quadratic formula

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# BECAUSE MOST OF US FORGET One possible application of this knowledge is to visualize the normal operation of a machine. Assuming the letter variable x = represents the deviation from normal operating temperature and the letter variable y = represents the deviation from normal operating pressure. Your given data says the center point assume your normal operating temperature (x = 3 degree ) and your normal operating pressure (y = 4 kPascal or kPa). Assuming the maintenance manual says normal temperature deviation (x1 = -1 degree) and your normal pressure deviation ( y1 = 3 kPa). Using your knowledge how to find the equation of a circle given its center point and one point on its circumference , you derived the equation of the circle as shown below. Now if you have data archive of your temperature and pressure from your computerized maintenance record, you can plot them using your derived equation and see how many times the machine is operating in normal operating region meaning inside the circle and how many times it is operating outside the normal region. Then maybe you can use this operational data to see the pattern and develop your machine learning algorithm in the future. This is just one imaginary application but you are free to assign variable letter x and y to any analog measurement values and associate it to machine attributes that you want to analyze. Find the equation of a circle with center point coordinate of (3,4) and a point P (-1,3)

Click input boxes to enter data

Center point coordinates (3,4)
( h , k )

Any Point coordinates, for example (-1,3) on its circumference
( x , y ) You can stop from here as your answer to equation of the circle.

( x - ) 2 + ( y - ) 2 = r 2 This radius, is still in the form r2. So take the square root of r,  r   to find the actual radius. Click the square root button

In generalized equation form of a circle which is: (x - h ) 2 + (y - k) 2 = r 2

First step is to solve for the value of r 2 . How to do that ?

Simply use the given value of x, y and h, k and simplify it to get the value of r 2

(-1-3) 2 + (3-4) 2 = r 2

(-4) 2 + (-1) 2 = r 2

16 + 1 = r 2

But if the requested solution is equation of a circle in simplified form then you need to expand the two binomial (x - h ) 2 and (y - k ) 2 then simplified the equation.

ANSWER after doing the binomial expansion of the above equation.

x2 - x + y2 - y + + =

ANSWER after simplifying the above equation

x2 - x + y2 - y + =

you can do additional simplification by subtracting 25 to both sides of equal sign. You should get - 8 as your constant on the right side of the equation.

Another method to find the equation of a circle is by using Geogebra software as shown below. Then follow the step by step instruction.

 Step Your browser does not support the canvas element. Delete point A, B, and C by selecting the three vertical dots. Then select delete Step Your browser does not support the canvas element. Enter in input box as is (3,4) next press enter tab. Drag the chart to the left so you can see the point A (3,4) Step Your browser does not support the canvas element. Enter in input box as is (-1, 3) next press enter tab. Move your graph to the left so you can see your two points. By clicking anywhere in your graph and continue pressing while dragging your mouse pointer to the left. Step Your browser does not support the canvas element. Select circle icon. Next select circle with center through point. Step Your browser does not support the canvas element. In your graph select point A as your center point. Next click point B. Equation of a circle will be displayed automatically on the left side. Answer is : (x -3 )2 + (y - 4)2 = 17 which is the same from manual calculation. You can also find the equation of any circle if you know its center point and the given radius. How ? Using Geogebra software, select circle with center and radius. That is your challenge question to learn how to do it given your acquired knowledge from this tutorial. Another challenge question is to find the equation of any circle given the three points on the circle's circumference.

Find first the equation of a circle. This is a simple explanation of machine learning. The computer algorithm will do automatic approximation by trial and error to discover the best fitting nearest neighbor by clustering in unsupervised machine learning. For human expert we only need two training points of data. The center point coordinate and any point around the circle and we discover the circle equation. Once the circle equation was discovered, it is use for prediction. Here the assumption is the behavior of ACTUAL data sets are within the confidence level with minimum error. Now you can see why learning Algebra and Analytical Geometry is useful. It saves you time for doing trial and error. It also save you waste in material and labor if your analysis is about material and labor expenses.

created by Apolinario "Sam" Ortega using Geogebra 3/24/2018

How do you know that learning happen in student's brain or knowledge was transferred to student's brain?

If the student can remember the procedural instruction how to solve the problem by using his memory only.

INVBAT.COM - A.I. + CHATBOT is very helpful for this kind of knowledge retrieval task because cloud technology have high speed , have large memory capacity and have fast computing power compared to human brain. Therefore human brain need Augmented Intelligence (Au.I.) to manage and control future advancement in Artificial Intelligence (Ar. I ) . Students, teachers, and employees today are busy they need on demand help to quickly review the procedural instruction. They also need automatic calculator for fast solution. By subscribing to INVBAT.COM - A.I. CHATBOT they will get on demand help using their smartphone, tablet, notebook, laptop, desktop, school smartboard, and even company smart T.V. in conference room.

INVBAT.COM -A.I. CHATBOT is solving previously impossible efficiency and convenience question. Example of impossible question 10 years ago, Can you combine formula and calculator make it available for immediate use using many devices? That is an impossible question 10 years ago ask by the founder of INVBAT.COM. Today that question is now considered as solved problem. You can help to grow the database of combined formula and calculator by subscribing or advertising to INVBAT.COM - A.I. + CHATBOT

Students are expected to master the attributes of circles and some of its applications:

CHATBOT ID number available for subscription ## INVBAT.COM - A.I. a disruptive innovation in computing and web search technology.

INVBAT.COM - A.I. is a disruptive innovation in computing and web search technology. For example scientific calculator help us speed up calculation but we still need to remember accurately the formula and the correct sequence of data entry. Here comes the disruptive innovation from INVBAT.COM-A.I. , today the problem of remembering formula and the correct sequence of data entry is now solved by combining formula and calculation and make it on demand using smartphone, tablet, notebook, Chromebook, laptop, desktop, school smartboard and company big screen tv in conference room with internet connection.

For web search , INVBAT.COM-A.I, is demonstrating that you can type text or use voice to text A.I. to search the web and get direct answer in one or two clicks. You don't need to waste your time looking from million of search results.
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