document.write( "Question 1081702: Find the equation that passes through (7,-4) at a distance of 1 unit from point (2,1). \n" ); document.write( "
Algebra.Com's Answer #695760 by Alan3354(69443)\"\" \"About 
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Find the equation that passes through A(7,-4) at a distance of 1 unit from point B(2,1).
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\n" ); document.write( "There are 2 lines.
\n" ); document.write( "They pass thru point A, and are tangent to a circle of radius 1 centered at (2,1).
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\n" ); document.write( "The angles at the tangent point between the line and radii are 90 degs.
\n" ); document.write( "2 right triangles are formed.
\n" ); document.write( "The hypotenuse, c, is the distance from A to B.
\n" ); document.write( "c = 5sqrt(2)
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\n" ); document.write( "The short side of the right triangles = 1.
\n" ); document.write( "The long sides, from A to the tangent points, = 7 units.
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\n" ); document.write( "Find the 2 tangent points:
\n" ); document.write( "The 2 points are the intersection of the 1 unit circle and a 7 unit circle centered at A.
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\n" ); document.write( "The unit circle is (x-2)^2 + (y-1)^2 = 1
\n" ); document.write( "The other circle is (x-7)^2 + (y+4)^2 = 49
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\n" ); document.write( "Solving those 2 will be messy.
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\n" ); document.write( "Do it like this:
\n" ); document.write( "Find the 2 angles at A:
\n" ); document.write( "tan = 1/7
\n" ); document.write( "The slope of AB is -1 --> the angle between the x-axis and AB = 135 degs.
\n" ); document.write( "The angles between the 2 lines and the x-axis are 135 ± atan(1/7)
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\n" ); document.write( "tan(135 + atan(1/7)) = (-1 + 1/7)/(1 - (-1)*(1/7)) = (-6/7)/(8/7) = -3/4
\n" ); document.write( "The tangent is the slope.
\n" ); document.write( "slope = -3/4
\n" ); document.write( "y+4 = (-3/4)*(x-7) is one of the lines.
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\n" ); document.write( "tan(135 - atan(1/7)) = (-1 - 1/7)/(1 + (-1)*(1/7)) = (-8/7)/(6/7) = -4/3
\n" ); document.write( "y+4 = (-4/3)*(x-7) is the other line.\r
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