PLEASE HELP ME. FIND THE EQUATION OF A CIRCLE PASSING THROUGH 
AND TANGENT TO THE LINES 
AND 
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document.write( "Draw the two lines and the point (3,7)\r\n" );
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document.write( "Those two lines intersect at (1,3).\r\n" );
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document.write( "Visually, it appears that there are two solutions:\r\n" );
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document.write( "Let's just look at one of them to keep things simple.\r\n" );
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document.write( "Suppose the center of the circle is (h,k)\r\n" );
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document.write( "The two green and the one red lines are radii of the desired\r\n" );
document.write( "circle. The two green radii represent the perpendicular (shortest)\r\n" );
document.write( "distances from (h,k) to each of the two lines.\r\n" );
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document.write( "The formula for the perpendicular distance from the point \r\n" );
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document.write( "(x1,y1)\r\n" );
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document.write( "to the line Ax+y+C=0 is\r\n" );
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document.write( "d = 
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document.write( "The lines are 1x-3y+8=0 and 3x-1y+0=0\r\n" );
document.write( "So for the first line A=1, B=-3, C=8\r\n" );
document.write( "For the second line A=3, B=-1, C=0\r\n" );
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document.write( "(x1,y1) = (h,k)\r\n" );
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= 
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= 
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= 
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document.write( "Multiplying through by 
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document.write( "|h-3k+8| = |3h-k|\r\n" );
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document.write( "There are two possibilities for that:\r\n" );
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document.write( "h-3k+8 = 3h-k and h-3k+8 = -(3h-k)\r\n" );
document.write( " -2k = 2h-8 h-3k+8 = -3h+k \r\n" );
document.write( " k = -h+4 -4k = -4h-8 \r\n" );
document.write( " k = 4-h k = h+2\r\n" );
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document.write( "Looking at the graph we can tell that \r\n" );
document.write( "the first one cannot be correct. because \r\n" );
document.write( "k=4-h would be saying that the sum of \r\n" );
document.write( "coordinates of (h,k), k+h = 4. The point\r\n" );
document.write( "(h,k) is even further to the right and\r\n" );
document.write( "higher than (1,3) where the two lines\r\n" );
document.write( "intersect. (1,3) has sum of coordinates \r\n" );
document.write( "4, so the sum of coordinates h and k has\r\n" );
document.write( "to be more than 4. Therefore \r\n" );
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document.write( "k = h+2.\r\n" );
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document.write( "Now we equate the red radius to one of the\r\n" );
document.write( "green radii. We use the distance formula between\r\n" );
document.write( "two points for the red radius:\r\n" );
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document.write( "d = √(x2-x1)²+(y2-y1)² \r\n" );
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document.write( " = 
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document.write( "Squaring both sides we have:\r\n" );
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= 
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document.write( "Multiplying both sides by 10\r\n" );
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document.write( "(3h-k)² = 10[(h-3)² + (k-7)²]\r\n" );
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document.write( "Substituting k = h+2 from above:\r\n" );
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document.write( "[3h-(h+2)]² = 10[(h-3)² + ((h+2)-7)²]\r\n" );
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document.write( "[3h-h-2]² = 10[(h-3)² + (h+2-7)²]\r\n" );
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document.write( "(2h-2)² = 10[(h-3)² + (h-5)²]\r\n" );
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document.write( "4h²-8h+4 = 10[h²-6h+9 + h²-10h+25]\r\n" );
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document.write( "4h²-8h+4 = 10(2h²-16h+34)\r\n" );
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document.write( "Divide both sides by 2\r\n" );
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document.write( "2h²-4h+2 = 5(2h²-16h+34)\r\n" );
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document.write( "2h²-4h+2 = 10h²-80h+170\r\n" );
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document.write( "-8h²+76h-168 = 0\r\n" );
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document.write( "Divide through by -4\r\n" );
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document.write( "2h²-19h+42 = 0\r\n" );
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document.write( "(2h-7)(h-6) = 0\r\n" );
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document.write( "2h-7 = 0; h-6 = 0\r\n" );
document.write( " 2h = 7; h = 6\r\n" );
document.write( " h = 
; \r\n" );
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document.write( "When h=, k = h+2 = +2 = 
= 
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document.write( "And the red radius = = 
= 
= \r\n" );
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= 
= 
= 
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document.write( "So the equation of one circle is\r\n" );
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document.write( "(x-h)²+(y-k)² = r²\r\n" );
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document.write( "That's one solution.\r\n" );
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document.write( "When h=6, k = h+2 = 6+2 = 8\r\n" );
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document.write( "And the red radius = = 
= 
= 
= \r\n" );
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document.write( "So the equation of the other circle is\r\n" );
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document.write( "(x-h)²+(y-k)² = r²\r\n" );
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document.write( "That's the other solution.\r\n" );
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document.write( "Edwin
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