document.write( "Question 986754: I really need help with this, would appreciate any help.\r
\n" ); document.write( "\n" ); document.write( "Show that the point E(-1 , 2) lies on the circumference of the circle with equation
\n" ); document.write( " x2 + y2 – 2x – 3y – 1 = 0 and find the coordinates of the point F,
\n" ); document.write( " given that EF is a diameter.
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Algebra.Com's Answer #607525 by Fombitz(32388) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"x%5E2-2x%2By%5E2-3y-1=0\"$
\n" ); document.write( " $\"%28-1%29%5E2-2%28-1%29%2B%282%29%5E2-3%282%29-1=0\"$
\n" ); document.write( " $\"1%2B2%2B4-6-1=0\"$
\n" ); document.write( " $\"0=0\"$
\n" ); document.write( "True, so point E satisfies the equation and therefore lies on the circle.
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\n" ); document.write( "Complete the square in x and y to find the center of the circle, $\"x%5E2-2x%2By%5E2-3y-1=0\"$
\n" ); document.write( " $\"%28x%5E2-2x%2B1%29%2B%28y%5E2-3y%2B9%2F4%29-1=1%2B9%2F4\"$
\n" ); document.write( " $\"%28x-1%29%5E2%2B%28y-3%2F2%29%5E2=2%2B9%2F4\"$
\n" ); document.write( " $\"%28x-1%29%5E2%2B%28y-3%2F2%29%5E2=17%2F4\"$
\n" ); document.write( "So the center of the circle is ( $\"1\"$ , $\"3%2F2\"$ )
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\n" ); document.write( "The x distance from E to the center is the same as the x distance from the center to F.
\n" ); document.write( " $\"d%5Bx%5D=1-%28-1%29=2\"$
\n" ); document.write( " $\"F%5Bx%5D=1%2B2=3\"$
\n" ); document.write( "Similarly for y,
\n" ); document.write( " $\"d%5By%5D=3%2F2-2=-1%2F2\"$
\n" ); document.write( " $\"F%5By%5D=3%2F2-1%2F2=1\"$
\n" ); document.write( "So point F is ( $\"3\"$ , $\"1\"$ )
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