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E.g. 5% charge on every 10% breach of the total breach of 102%. Any short summed-up formula?
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ou’ll be using the same 4 numbers written in the same order. The only thing that will change in each expression will be the tools you’ll use from your toolbox. The tools that you’ve learned so far for order of operations are parentheses, exponents, multiplying, dividing, adding, and subtracting. Here are the four numbers. Keep them in this order: 18 2 4 3 Here are the tools in your toolbox: The 2 and 3 represent exponents, so you are allowed to square or cube a number. Listed below are the values you need to create. 21 = 67 = -6 = 103 =
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Equation of a Circle

The equation of a circle maps the circle on a two-dimensional coordinate plane. Following are some useful forms of the equation of the circle.
 

Standard Form

(x-h)2+(y-k)= r2

Where h,k is the coordinate of the center of the circle, and r is the radius.

Polar Form 

x2+y= r2

Where x=rcosθ and y=rsinθ.

General Form 

x2+y2+Ax+By+C = 0

Where A, B, and C are constant.

 

Equation of a Circle Sample Questions:

Question 1: What would be the center of the following equation of the circle?


(x-2)2+(y-3)= 62


Answer: (2,3)

Explanation: Use the formula of standard form of the equation of a circle.

 

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Question 2: What would be the radius of the following equation of the circle?


(x-5)2+(y-7)= 49


Answer: 7 units

Explanation: Use the formula of standard form of the equation of a circle.

 

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Question 3: Write the equation of circle in standard form for the following figure:


Graph 4


Answer:  (x-3)2+(y-2)= 32

Explanation: The given figure has the center as 3,2 and radius as r=3 units.
Now, let us plug those values, we get.

 

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Question 4: Identify the center and radius of the circle, and sketch its graph:


(x+1)2+(y-2)= 16


Graph 2


Answer: Graph 3

Explanation: Use the formula of standard form of the equation of a circle.

 

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Question 5: Translate the following equation of circle by 4 units right, 2 units down  (x+3)2+(y-5)= 25.


Answer: (x+7)2+(y-3)= 25

Explanation: Translate the 4 units down and then translate 2 units down.

 

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Question 6: Translate the following equation of circle by 3 units left, 5 units up  (x+3)2+(y-5)= 64.

Answer: (x)2+(y)= 64

Explanation: Translate the 3 units down and then translate 5 units up.

 

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Question 7: Identify the center and radius of the circle, and sketch its graph:


(x-2)2+(y+3)= 9


Graph


Answer: Graph 1


Center is at 2,-3 and radius as r=3 units

Explanation: Use the formula of standard form of the equation of a circle.

 

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Question 8: Write the following equation of the circle in standard form


x2+ 8x - 2y = 64 - y2


Answer: (x+4)2+(y+1)= 81

Explanation: Rewrite the equation and complete the square.

 

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Question 9: Write the following equation of the circle in polar form.


x2+ 7x + y2 - 5y = 0

 

Answer: r=-8cosθ + 2sinθ

Explanation: Plug x+ y= r2, and x=rcosθ, y=rsinθ

 

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Question 10: Write the following equation of the circle in polar form.


x- 9x + y2 + 5y = 0


Answer: r=9cosθ - 5sinθ

Explanation: Plug x+ y= r2, and x=rcosθ, y=rsinθ

 

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