Lösung 4.1:5a
Aus Online Mathematik Brückenkurs 1
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Version vom 14:46, 22. Okt. 2008
A circle is defined as all the points which have a fixed distance to the circle's midpoint. Hence, a point (x,y) lies on our circle if and only if its distance to the point (1,3) is exactly 2. Using the distance formula, we can express this condition as
| \displaystyle \sqrt{(x-1)^2 + (y-2)^2} = 2\,\textrm{.} |
After squaring, we obtain the equation of the circle in standard form,
| \displaystyle (x-1)^2 + (y-2)^2 = 4\,\textrm{.} |
