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Added Diametric Form (#28445)

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* Added Diametric Form

* fix: format formulas
This commit is contained in:
Abhishek Narang
2019-06-28 07:28:51 +05:30
committed by Randell Dawson
parent c6e4efc268
commit 3bb3ea1a98
1 changed files with 14 additions and 2 deletions
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guide/english/mathematics/circle-equations/index.md
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@ -35,7 +35,19 @@ for,
![0<=t<= 2 pi](https://raw.githubusercontent.com/pranabendra/articles/master/geometry/circle/circle_5.png) ![0<=t<= 2 pi](https://raw.githubusercontent.com/pranabendra/articles/master/geometry/circle/circle_5.png)
### 3. Diametric form:
Suppose there are two points on a circle (x1, y1) and (x2, y2), such that they lie on the opposite ends of the same diameter. Then the equation of circle can be written as:
```
(x-x1)(x-x2) + (y-y1)(y-y2) = 0
```
Suppose 2 points on the circle A = (x1, y1) and B = (x2, y2) are diametrically opposite, then for any point C = (x,y) on the circle, ΔABC will be a right triangle with right angle at C. This implies
```
AC ⊥ BC
(mAC)*(mBC) = -1
```
Substituting the values for slopes, we get: (x-x1)(x-x2) + (y-y1)(y-y2) = 0
### More Information: ### More Information:
<a href = "http://mypages.valdosta.edu/alazari/math1111/Circle.html" target="_blank" rel="nofollow">Equation of a Circle</a> <a href = "http://mypages.valdosta.edu/alazari/math1111/Circle.html" target="_blank" rel="nofollow">Equation of a Circle</a>