Lösung 4.1:5a

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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
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
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{{Displayed math||<math>\sqrt{(x-1)^2 + (y-2)^2} = 2\,\textrm{.}</math>}}
+
{{Abgesetzte Formel||<math>\sqrt{(x-1)^2 + (y-2)^2} = 2\,\textrm{.}</math>}}
After squaring, we obtain the equation of the circle in standard form,
After squaring, we obtain the equation of the circle in standard form,
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{{Displayed math||<math>(x-1)^2 + (y-2)^2 = 4\,\textrm{.}</math>}}
+
{{Abgesetzte Formel||<math>(x-1)^2 + (y-2)^2 = 4\,\textrm{.}</math>}}
[[Image:4_1_5_a.gif|center]]
[[Image:4_1_5_a.gif|center]]

Version vom 08:48, 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{.}


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