document.write( "Question 697785: find the equation of circle whose center lies on the line x=2y;passes through (2,1)and the length of the tangent from origin is radical 7(seven) ; please i am so tierd with this question help me \n" ); document.write( "

Algebra.Com's Answer #430287 by AnlytcPhil(1806) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "Let the equation be \r\n" );
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document.write( "(1)     (x-h)² + (y-k)² = r²\r\n" );
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document.write( "and since it is on the line 2y=x,\r\n" );
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document.write( "(2)     2k = h\r\n" );
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document.write( "(2,1) is on the circle and also on the line 2y=x\r\n" );
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document.write( "So (2,1) satisfies the equation of the circle, so\r\n" );
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document.write( "        (2-h)² + (1-k)² = r²\r\n" );
document.write( "        4-4h+h²+1-2k+k² = r²\r\n" );
document.write( "(3)         h²+k²-4h-2k = r²-5 \r\n" );
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document.write( "By the distance formula OC² = h²+k² \r\n" );
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document.write( "OCT is a right triangle because a tangent is perpendicular\r\n" );
document.write( "to the radius drawn to the point of tangency. So using\r\n" );
document.write( "the Pythagorean theorem:\r\n" );
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document.write( "        OC² = TC² + OT² \r\n" );
document.write( "        h²+k² = r²+ \r\n" );
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document.write( "(4)       h²+k² = r²+7     \r\n" );
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document.write( "Subtracting equation (4) from equation (3) gives\r\n" );
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document.write( "         -4h-2k = -12  or\r\n" );
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document.write( "(5)       2h+k = 6\r\n" );
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document.write( "Using (2), (5) becomes\r\n" );
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document.write( "       2(2k)+k = 6\r\n" );
document.write( "          4k+k = 6\r\n" );
document.write( "            5k = 6\r\n" );
document.write( "             k = \r\n" );
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document.write( "Using (2), h = 2·\r\n" );
document.write( "           h = \r\n" );
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document.write( "So the center C(h,k) = C(,)\r\n" );
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document.write( "We just need to find r²\r\n" );
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document.write( "Using (4)\r\n" );
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document.write( "          h²+k² = r²+7\r\n" );
document.write( "         + = r²+7\r\n" );
document.write( "         + = r²+7\r\n" );
document.write( "          = r²+7\r\n" );
document.write( "          = r²+7\r\n" );
document.write( "         -7 = r²\r\n" );
document.write( "         - = r²\r\n" );
document.write( "          = r²\r\n" );
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document.write( "So we can write the equation of the circle as\r\n" );
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document.write( "        (x-h)² + (y-k)² = r²\r\n" );
document.write( "        {x-)² + (y-)² = \r\n" );
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document.write( "If you like you can square those out, collect terms and clear of \r\n" );
document.write( "fractions and you'll end up with\r\n" );
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document.write( "        5x² + 5y² - 24x - 12y + 35 = 0\r\n" );
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document.write( "Edwin

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