Processing Math: Done
Solution 4.1:5b
From Förberedande kurs i matematik 1
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+ | If the circle is to contain the point | ||
+ | <math>\left( -1 \right.,\left. 1 \right)</math>, then that point's distance away from the centre | ||
+ | <math>\left( 2 \right.,\left. -1 \right)</math> | ||
+ | must equal the circle's radius, | ||
+ | <math>r</math>. Thus, we can obtain the circle's radius by calculating the distance between | ||
+ | <math>\left( -1 \right.,\left. 1 \right)</math> | ||
+ | and | ||
+ | <math>\left( 2 \right.,\left. -1 \right)</math> | ||
+ | using the distance formula: | ||
+ | |||
+ | |||
+ | <math>\begin{align} | ||
+ | & r=\sqrt{\left( 2-\left( -1 \right) \right)^{2}+\left( -1-1 \right)^{2}}=\sqrt{3^{2}+\left( -2 \right)^{2}} \\ | ||
+ | & =\sqrt{9+4}=\sqrt{13} \\ | ||
+ | \end{align}</math> | ||
+ | |||
+ | |||
+ | When we know the circle's centre and its radius, we can write the equation of the circle, | ||
+ | |||
+ | |||
+ | <math>\left( x-2 \right)^{2}+\left( y-\left( -1 \right) \right)^{2}=\left( \sqrt{13} \right)^{2}</math> | ||
+ | |||
+ | |||
+ | which the same as | ||
+ | |||
+ | |||
+ | <math>\left( x-2 \right)^{2}+\left( y+1 \right)^{2}=13</math> | ||
+ | |||
{{NAVCONTENT_START}} | {{NAVCONTENT_START}} | ||
[[Image:4_1_5_b-1(2).gif|center]] | [[Image:4_1_5_b-1(2).gif|center]] | ||
- | <center> [[Image:4_1_5b-1(2).gif]] </center> | ||
- | {{NAVCONTENT_STOP}} | ||
- | {{NAVCONTENT_START}} | ||
- | <center> [[Image:4_1_5b-2(2).gif]] </center> | ||
{{NAVCONTENT_STOP}} | {{NAVCONTENT_STOP}} | ||
+ | |||
+ | NOTE: A circle having its centre at | ||
+ | <math>\left( a \right.,\left. b \right)</math> | ||
+ | and radius | ||
+ | <math>r</math> | ||
+ | has the equation | ||
+ | |||
+ | |||
+ | <math>\left( x-a \right)^{2}+\left( y-b \right)2=r^{2}</math> |
Revision as of 11:20, 27 September 2008
If the circle is to contain the point
−1
1
2
−1
−1
1
2
−1
2−
−1
2+
−1−1
2=
32+
−2
2=
9+4=
13
When we know the circle's centre and its radius, we can write the equation of the circle,
x−2
2+
y−
−1
2=
13
2
which the same as
x−2
2+
y+1
2=13
NOTE: A circle having its centre at
a
b
x−a
2+
y−b
2=r2