document.write( "Question 1124597: The centre of a circle is on the line y=2x-3. The circle also passes through A(5,2) and B(3,-2). Determine the equation of the circle. \n" ); document.write( "
Algebra.Com's Answer #740921 by MathLover1(20855)\"\" \"About 
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a circle is on the line \"y=2x-3\" and also passes through A(\"5\",\"2\") and B(\"3\",\"-2\")\r
\n" ); document.write( "\n" ); document.write( "graph a line and given points:\r
\n" ); document.write( "\n" ); document.write( "\"y=2x-3\"\r
\n" ); document.write( "\n" ); document.write( "\"x\"|\"y\"
\n" ); document.write( "\"0\"|\"-3\"
\n" ); document.write( "\"x\"|\"0\"->\"0=2x-3\"->\"3=2x\"->\"x=3%2F2\"\r
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\n" ); document.write( "\n" ); document.write( "find coordinates of the midpoint of A(\"5\",\"2\") and B(\"3\",\"-2\")\r
\n" ); document.write( "\n" ); document.write( "(\"%285%2B3%29%2F2\",\"%282-2%29%2F2\")\r
\n" ); document.write( "\n" ); document.write( "(\"4\",\"0\")...use it to find equation of a line perpendicular to the line \"y=2x-3\"-> slope is \"m=2\"\r
\n" ); document.write( "\n" ); document.write( "perpendicular lines have slopes negative reciprocal to each other\r
\n" ); document.write( "\n" ); document.write( "so, our perpendicular line, \"y=mx%2Bb\", will have a slope \"m%5Bp%5D=-1%2F2\"\r
\n" ); document.write( "\n" ); document.write( "\"y=-%281%2F2%29x%2Bb\"...to find \"b\" plug in coordinates of the midpoint (\"4\",\"0\")\r
\n" ); document.write( "\n" ); document.write( "\"0=-%281%2F2%294%2Bb\"\r
\n" ); document.write( "\n" ); document.write( "\"0=-%281%2Fcross%282%29%29cross%284%292%2Bb\"\r
\n" ); document.write( "\n" ); document.write( "\"0=-2%2Bb\"\r
\n" ); document.write( "\n" ); document.write( "\"b=2\"\r
\n" ); document.write( "\n" ); document.write( "line is:\r
\n" ); document.write( "\n" ); document.write( "\"y=-%281%2F2%29x%2B2\"\r
\n" ); document.write( "\n" ); document.write( "let's add it to the graph\r
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\n" ); document.write( "\n" ); document.write( "the point where lines \"y=2x-3\" and \"y=-%281%2F2%29x%2B2\" should intersect in one point which is the center o the circle\r
\n" ); document.write( "\n" ); document.write( "\"y=2x-3\"
\n" ); document.write( "\"y=-%281%2F2%29x%2B2\"
\n" ); document.write( "-------------------solve system; since left sides are same, we have\r
\n" ); document.write( "\n" ); document.write( "\"2x-3=-%281%2F2%29x%2B2\" ...solve or \"x\"\r
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\n" ); document.write( "\n" ); document.write( "\"2x%2B%281%2F2%29x=3%2B2\"\r
\n" ); document.write( "\n" ); document.write( "\"2x%2B%281%2F2%29x=5\"...both sides multiply by \"2\"\r
\n" ); document.write( "\n" ); document.write( "\"4x%2Bx=10\"\r
\n" ); document.write( "\n" ); document.write( "\"5x=10\"\r
\n" ); document.write( "\n" ); document.write( "\"x=2\"\r
\n" ); document.write( "\n" ); document.write( "now find \"y\"\r
\n" ); document.write( "\n" ); document.write( "\"y=2%2A2-3\"
\n" ); document.write( "\"y=1\"\r
\n" ); document.write( "\n" ); document.write( "so, intersection point is: C(\"2\",\"1\")=>\"h=2\" and \"k=1+\" coordinates o the center\r
\n" ); document.write( "\n" ); document.write( "add to graph\r
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\n" ); document.write( "\n" ); document.write( "now we need radius \"r\"
\n" ); document.write( "since circle also passes through A(\"5\",\"2\") and B(\"3\",\"-2\"), use one of these points and find distance between that point and center\r
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\n" ); document.write( "\n" ); document.write( "C(\"2\",\"1\")
\n" ); document.write( "A(\"5\",\"2\")\r
\n" ); document.write( "\n" ); document.write( "\"r=sqrt%28%28x%5B2%5D-x%5B1%5D%29%5E2%2B%28y%5B2%5D-y%5B1%5D%29%5E2%29\"\r
\n" ); document.write( "\n" ); document.write( "\"r=sqrt%28%285-2%29%5E2%2B%282-1%29%5E2%29\"\r
\n" ); document.write( "\n" ); document.write( "\"r=sqrt%283%5E2%2B1%5E2%29\"\r
\n" ); document.write( "\n" ); document.write( "\"r=sqrt%2810%29\"\r
\n" ); document.write( "\n" ); document.write( "\"r=3.16\"\r
\n" ); document.write( "\n" ); document.write( "add circle to the graph\r
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\n" ); document.write( "\n" ); document.write( "and, your equation of the circle is: \r
\n" ); document.write( "\n" ); document.write( "\"%28x-h%29%5E2%2B%28y-k%29%5E2=r%5E2\" where \"h\" and \"k+\" coordinates o the center, \"+r+\"is radius\r
\n" ); document.write( "\n" ); document.write( "plug in values:C(\"2\",\"1\")=>\"h=2\" and \"k=1+\" and \"r%5E2=10\"\r
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\n" ); document.write( "\n" ); document.write( "\"%28x-2%29%5E2%2B%28y-1%29%5E2=10\"\r
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