document.write( "Question 1140359: Consider the circle x^2 + y^2 - 2x -14y +25=0
\n" ); document.write( "Show that, if the line y=mx intersects the circle in two distinct points, then (1+7m)^2 -25(1+m^2) > 0 \n" ); document.write( "

Algebra.Com's Answer #760916 by ikleyn(52810) $\"\"$ $\"About$

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document.write( "Substitute  y = mx  into the given equation of the circle and combine common terms.\r\n" );
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document.write( "The condition that the straight line intersects the circle in two points is equivalent to the fact that \r\n" );
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document.write( "the obtained quadratic equation has two real roots.\r\n" );
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document.write( "In turn, it means that the discriminant of this quadratic equation is POSITIVE.\r\n" );
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document.write( "The condition that the discriminant is positive is exactly the inequality of your post.\r\n" );
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