From Förberedande kurs i matematik 1

Revision as of 13:02, 2 April 2008 (edit) Oskar (Talk | contribs) (Ny sida: {{NAVCONTENT_START}} <center> Bild:4_1_5b-1(2).gif </center> {{NAVCONTENT_STOP}} {{NAVCONTENT_START}} <center> Bild:4_1_5b-2(2).gif </center> {{NAVCONTENT_STOP}}) ← Previous diff		Current revision (10:53, 7 October 2008) (edit) (undo) Tek (Talk | contribs) m
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-	{{NAVCONTENT_START}}	+	If the circle is to contain the point (-1,1), then that point's distance away from the centre (2,-1) must equal the circle's radius, ''r''. Thus, we can obtain the circle's radius by calculating the distance between (-1,1) and (2,-1) using the distance formula,
-	<center> [[Bild:4_1_5b-1(2).gif]] </center>	+
-	{{NAVCONTENT_STOP}}	+	{{Displayed math||<math>\begin{align}
-	{{NAVCONTENT_START}}	+	r &= \sqrt{(2-(-1))^2+(-1-1)^2} = \sqrt{3^2+(-2)^2} = \sqrt{9+4} = \sqrt{13}\,\textrm{.}
-	<center> [[Bild:4_1_5b-2(2).gif]] </center>	+	\end{align}</math>}}
-	{{NAVCONTENT_STOP}}	+
		+	When we know the circle's centre and its radius, we can write the equation of the circle,
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		+	{{Displayed math||<math>(x-2)^2 + (y-(-1))^2 = (\sqrt{13})^{2}</math>}}
		+
		+	which the same as
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		+	{{Displayed math||<math>(x-2)^{2} + (y+1)^2 = 13\,\textrm{.}</math>}}
		+
		+
		+	[[Image:4_1_5_b-1(2).gif|center]]
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		+	Note: A circle having its centre at (''a'',''b'') and radius ''r'' has the equation
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		+	{{Displayed math||<math>(x-a)^2 + (y-b)^2 = r^2\,\textrm{.}</math>}}

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Current revision

If the circle is to contain the point (-1,1), then that point's distance away from the centre (2,-1) must equal the circle's radius, r. Thus, we can obtain the circle's radius by calculating the distance between (-1,1) and (2,-1) using the distance formula,

\displaystyle \begin{align} r &= \sqrt{(2-(-1))^2+(-1-1)^2} = \sqrt{3^2+(-2)^2} = \sqrt{9+4} = \sqrt{13}\,\textrm{.} \end{align}

When we know the circle's centre and its radius, we can write the equation of the circle,

\displaystyle (x-2)^2 + (y-(-1))^2 = (\sqrt{13})^{2}

which the same as

\displaystyle (x-2)^{2} + (y+1)^2 = 13\,\textrm{.}

Note: A circle having its centre at (a,b) and radius r has the equation

\displaystyle (x-a)^2 + (y-b)^2 = r^2\,\textrm{.}