The base equation for a circle centered at (h,k) with radius r is:

   (x - h)²+ (y - k)² = r²

If the points are concyclic, they all lie on the graph for the same circle.

Thus, all points are solutions to a single equation of the circle

WE can plug each point into the base equation, and obtain a system of equationd

FOR POINT (-2,10)

     Equation 1:  (-2 - h)² + (10 - k)² = r²

FOR POINT (1,11)

     Equation 2:  (1 - h)²+ (11 - k)² = r²

FOR POINT (6,10)

     Equation 3:  (6 - h)² + (10 - k)² = r²

FOR POINT (9,7)

     Equation 4:  (9 - h)² + (7 - k)² = r²

From Equation 1 and 2 above, since they have 2 different expressions equivalent to r2, we can construct an equation involving variables x and h.

     r² = r²   

     (-2 - h)² + (10 - k)² = (1 - h)² + (11 - k)²

     (-2 - h)(-2 - h) + (10 - k)(10 - k) = (1 - h)(1 - h) + (11 - k)(11 - k)

     (4 + 2h + 2h + h²) + (100 -10k - 10k + k²) = (1 - h - h + h²) + (121 - 11k - 11k + k²)

      h² + 4h + 4 + k² - 20k + 100 = h²-2h + 1 + k² -22k + 121

    We can subtract h and k from both sides.

      4h + 4 - 20k + 100 = -2h + 1 -22k + 122

      4h -20k + 104 = -2h - 22k + 122

    Move all h and k variables to the left ... move all constants to the right

      6H + 2K = 18

SYSTEM EQUATION 1:   6h + 2k = 18      

From equation 3 and 4 above, we go through the same process to obtain a second system equation.

       r² = r²

       (6 - h)² + (10 - k)² = (9 - h)² + (7 - k)²

       (6 - h)(6 - h) + (10 - k)(10 - k) = (9 - h)(9 - h) + (7 - k)(7 - k)

       36 - 6h - 6h + h²+ 100 - 10k - 10k + k² = 81 - 9h - 9h + h² + 49 = 7k - 7k + k²

       h² - 12h + 36 + k² - 20k + 100 = h² - 18h + 81 + k²- 14k + 49

    Simplify, and subtract h2 and k2from both sides

       -12h - 20k + 136 = -18h - 14k + 130

      Move the h and k variables to the left, and the constants to the right

        -12h + 18h - 20k + 14k = 130 - 136

        6h - 6k = -6

SYSTEM EQUATION 1:  6h - 6k = -6

      6h +2k = 18

      6h - 6k = -6

Multiply the second equation by -1, we have ... -6h + 6k = 6

Adding the 2 equations, we have

 6h + 2k = 18

  -6h + 6k =  6

          8k =24

             k = 3

Using substitution of k=3 into equation 6h + 2k = 18,
   
6h + 2(3) = 18

    6h + 6 = 18

    6h = 12

    h = 2

Now, use one of the points on the circle ... (1, 11) and (h,k) ... (2,3), to find the radius

   (1 - 2)² + (11 - 3)² = r²

   1 + 64 = r²

   65 = r²

   r = √65
Thus the equation of our circle is:
   (x - 2)² + (y - 3)² = (√65)²

Book keeping is stated as the recording of day-to-day business transactions in the books of accounts. It involves identification of transactions of financial nature, recording them in the books of accounts and classifying them into the ledger accounts.

Correlation is a statistical tool which studies the relationship between two variables e.g. change in price leads to change in quantity demanded.
Correlation studies and measures the direction and intensity of relationship among variables. It measures co-variation not causation. It does not imply cause and effect relation.

Type of Correlation
Correlation is classified into positive and negative correlation. The correlation is said to be positive when the variables move together in the same direction. e.g. sale of lce cream and temperature move in same direction.
The correlation is said to be negative when the variables move in opposite direction. e.g. When you spend more time in studying chances of your failure decline.

Electric Current is the flow of electrons. But an electric Circuit is the closed path in which electric current flows.

• When an electric current flows through a wire, the wire gets heated. It is the heating effect of current or When current flows through a metal wire it gets heated up, this is called heating effect of current. E.g. a glowing electric bulb becomes warm. This effect has many applications like Electric Heater, Light Bulb etc.
• When an electric current flows through a wire, it produces magnetic effect around it. A current carrying coil of an insulated wire wrapped around a piece of iron is called an electromagnet. Magnetic Effect of electric current has many applications like Electric Bell, Motor, Fan etc

Auxins

• IAA and indole butyric acid (IBA) have been isolated from plants and NAA (naphthalene acetic acid) and 2, 4-D (2, 4-dichlorophenoxyacetic) are synthetic auxins.
• They help to initiate rooting in stem cuttings, promote flowering, prevent fruit and leaf drop at early stages, induce parthenocarpy (example- tomato).
• In most higher plants, the growing apical bud inhibits the growth of the lateral (axillary) buds, a phenomenon called apical dominance.
• Auxins are widely used as herbicides.

Example- 2, 4-D is widely used to kill dicotyledonous weeds.

Gibberellins

• Gibberellins are denoted as GA₁, GA₂, GA₃.
• All gibberellins are acidic.
• They help to increase in length of axis, elongate and improve shape of fruits, delay senescence,
• Spraying juvenile conifers with GAs hastens the maturity period, thus leading to early seed production.
• Gibberellins also promotes bolting, defined as internode elongation just prior to flowering, in beet, cabbages.

Cytokinins

• Cytokinins were discovered as kinetin from the autoclaved herring sperm DNA.
• Natural cytokinins are synthesised in regions where rapid cell division occurs, for example, root apices.

Internal energy is a state function i.e. depends only upon the state of the system and is independent of the method by which this state has been attained.

Let us change the internal energy of the system by doing work called adiabatic work. This can be done in two ways:

(1) By doing mechanical work by rotating a set of small paddles.

(2) By doing electrical work with the help of an immersion rod.

Orbital velocity is the velocity given to artificial satellite so that it may start revolving around the earth.

Features of Foreign Trade

• Negative Trade
• Changing Imports
• Diversity in Exports
• Trading through Selected Ports
• Trade during Maritime
• Worldwide Trade
• Place of India in Overseas Trade

“A Bill of Exchange is an instrument in writing containing an unconditional order signed by the maker, directing a certain person to pay a certain sum of money only to, or the order of, a certain person or to the bearer of the instrument.” Section 5 of the Negotiable Instrument Act, 1881

Features of a Bill Exchange are:

1. A bill of exchange must be in writing

2. It must contain an order (and note a request) to make payment.

3. The order of payment must be unconditional.

4. The amount of bill of exchange must be certain.

5. The date of payment should be certain.

The presence or absence of pigments is the main basis of classification of algae.

Chlorophyceae: Chlorophyll a and b are present in them and impart green colour. Chlorophyceae are also called ‘blue-green algae’.

Phaeophyceae: Chlorophyll a and c and fuxoxanthin are present. Fucoxanthin imparts brown colour. Phaeophyceae are also called ‘brown algae’.

Rhodophyceae: Chlorophyll a and d and phycoerythrin are present. Phycoerythrin imparts red colour. Rhodophyceae are also called ‘red algae’.