document.write( "Question 1087984: Hi there,really stumped by this question. For a circle with the equation x^2 + y^2 - 2x - 14y + 25 = 0, show that if the line y = mx + c intersects the circle at two points, then (1 + 7m)^2 - 25(1 + m^2) > 0.
\n" ); document.write( "I can work out the centre of the circle to be (1,7) and the radius as 5, but I cannot see that helps.
\n" ); document.write( "Paul
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Algebra.Com's Answer #702258 by ikleyn(52817)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "1.  Substitute y = mx +c into the second degree equation, replacing y. You will get\r\n" );
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document.write( "    \"%28mx%2Bc%29%5E2+-+2x+-+14%28mx%2Bc%29+%2B+25\" = 0.\r\n" );
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document.write( "2.  Simplify the last equation and reduce it to the standard form of a quadratic equation\r\n" );
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document.write( "    ax^2 + bx + c = 0.\r\n" );
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document.write( "3.  The fact that  \"the line y = mx + c intersects the circle at two points\"  means that this quadratic equation has \r\n" );
document.write( "    two different real solutions.\r\n" );
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document.write( "4.  This, in turn, means that the discriminant of the quadratic equation is POSITIVE: d = b^2 - 4ac > 0.\r\n" );
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document.write( "5.  This inequality is exactly what you need to prove.\r\n" );
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\n" ); document.write( "\n" ); document.write( "I completed my tutor's instructions.\r
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\n" ); document.write( "\n" ); document.write( "You implement this guiding idea.\r
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