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標題:
圓形 : x ^2 + y^2 = r^2
發問:
圓形 : x ^2 + y^2 = r^2 <------這formula在說什麼?代表什麼?怎得出來? 謝謝謝謝 更新: 呢樣野係幾時學嫁?中幾學? (邊個topic教?) 條formula有咩用?
最佳解答:
In your case, this formula tells us that this is a circle, centre (0,0) and radius r. It might be easier to understand if you write it like this: (x-a)^2 + (y-b)^2 = r^2 Where the centre of the circle is (a,b) and radius is r. Example 1: Find the equation of a circle centre (1,-2), radius 3. (x-1)^2 + [y-(-2)]^2 = 3^2 (x-1)^2 +(y+2)^2 = 9 Example 2: Find the centre and the radius of circle with equation, (x+4)^2 + (y-5)^2 = 36 Centre (-4, 5) and radius 6. As for how you get this equation, it is quite simple if you follow this: 1) x, y are any points on the circle 2) a, b are the centre of the circle 3) r is the radius of the circle 4) if you calculate the radius r by Pythagora's (p^2 + q^2 = r^2), you would know that (x-a) is the 'x' distance, (y-b) is the 'y' distance. (x-a), (y-b) and r (the radius) form a right triangle, so then you can use p^2 + q^2 = r^2. In this case, (x-a)^2 + (y-b)^2 = r^2 I hope this helps, I know I should probably type in Chinese, but I'm really bad at typing Chinese (there are many characters that I don't know how to type).. So I hope this is OK! :)
圓形 : x ^2 + y^2 = r^2
發問:
圓形 : x ^2 + y^2 = r^2 <------這formula在說什麼?代表什麼?怎得出來? 謝謝謝謝 更新: 呢樣野係幾時學嫁?中幾學? (邊個topic教?) 條formula有咩用?
最佳解答:
In your case, this formula tells us that this is a circle, centre (0,0) and radius r. It might be easier to understand if you write it like this: (x-a)^2 + (y-b)^2 = r^2 Where the centre of the circle is (a,b) and radius is r. Example 1: Find the equation of a circle centre (1,-2), radius 3. (x-1)^2 + [y-(-2)]^2 = 3^2 (x-1)^2 +(y+2)^2 = 9 Example 2: Find the centre and the radius of circle with equation, (x+4)^2 + (y-5)^2 = 36 Centre (-4, 5) and radius 6. As for how you get this equation, it is quite simple if you follow this: 1) x, y are any points on the circle 2) a, b are the centre of the circle 3) r is the radius of the circle 4) if you calculate the radius r by Pythagora's (p^2 + q^2 = r^2), you would know that (x-a) is the 'x' distance, (y-b) is the 'y' distance. (x-a), (y-b) and r (the radius) form a right triangle, so then you can use p^2 + q^2 = r^2. In this case, (x-a)^2 + (y-b)^2 = r^2 I hope this helps, I know I should probably type in Chinese, but I'm really bad at typing Chinese (there are many characters that I don't know how to type).. So I hope this is OK! :)
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