document.write( "Question 974270: find the equation of the circle in the fourth quadrant whose diameter is 8 and is tangent to both axes. \n" ); document.write( "

Algebra.Com's Answer #596227 by KMST(5328) $\"\"$ $\"About$

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If the diameter is $\"8\"$ , the radius must be $\"8%2F2=4\"$ .
\n" ); document.write( "The radii at the point of tangency with both axes, and the axes form a quadrilateral.
\n" ); document.write( "The radius at the points of tangency with each axis is perpendicular to that axis, so the quadrilateral has two right angles at the points of tangency.
\n" ); document.write( "Since the axes are perpendicular to each other,
\n" ); document.write( "the quadrilateral has a third right angle at the origin.
\n" ); document.write( "The fourth angle (at the center of the circle) has to also be a right angle,
\n" ); document.write( "because the measures of the interior angles of a quadrilateral add up to $\"360%5Eo\"$ .
\n" ); document.write( "So that quadrilateral is a rectangle,
\n" ); document.write( "but since those radii at the points of tangency are
\n" ); document.write( "adjacent sides of the rectangle, and each one has a length of $\"4\"$ ,
\n" ); document.write( "that rectangle is a square,
\n" ); document.write( "and the center of the circle is at (4,-4).
\n" ); document.write( "

The equation is $\"%28x-4%29%5E2%2B%28y%2B4%29%5E2=4%5E2\"$ <--> $\"%28x-4%29%5E2%2B%28y%2B4%29%5E2=16\"$ \n" ); document.write( "

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