document.write( "Question 714404: Find the equation of the circle passing through (2,2) and tangent to the line y=1 and y= 6 \n" ); document.write( "

Algebra.Com's Answer #438824 by htmentor(1343) $\"\"$ $\"About$

You can put this solution on YOUR website!
The tangent lines touch the circle at the top and the bottom.
\n" ); document.write( "This means that the diameter of the circle is the distance between the two tangent lines 6-1=5.
\n" ); document.write( "So r = 2.5, and the center of the circle lies halfway in between y=1 and y=6.
\n" ); document.write( "So the center has the coordinates (a,3.5) and the radius is 2.5:
\n" ); document.write( "(x-a)^2 + (y-3.5)^2 = 2.5^2
\n" ); document.write( "We can use the point (2,2) on the circle to find a:
\n" ); document.write( "(2-a)^2 + (2-3.5)^2 = 2.5^2
\n" ); document.write( "This simplifies to a^2 - 4a = 0
\n" ); document.write( "a(a-4) = 0
\n" ); document.write( "There are two possibilities, a=0 and a=4.
\n" ); document.write( "So there are two circles which fit the criteria:
\n" ); document.write( "x^2 + (y-3.5)^2 = 6.25
\n" ); document.write( "(x-4)^2 + (y-3.5)^2 = 6.25 \n" ); document.write( "

\n" );