document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=596072>Question 596072</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A circle has its center at(4,0) and a radius of 5 units. Which quadrants does the circle pass through. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #377495 by </B><A HREF=/tutors/aboutme.mpl?userid=math-vortex><B>math-vortex(648)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math-vortex><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=math-vortex><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=377495\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Hi, there--<BR>\n" );
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document.write( "This circle passes through all four quadrants. Here's why:<BR>\n" );
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document.write( "[I] Quadrant I <BR>\n" );
document.write( "The center of this circle is at (4,0) on the x-axis. Since the radius is 5 units, every point on the circle is exactly 5 units from (4,0). The point (4,5) is 5 units directly above (4,0). We can see that (4,5) is in quadrant I because the x- and y-coordinates are both positive.<BR>\n" );
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document.write( "{II}Quadrant IV<BR>\n" );
document.write( "Using similar reasoning, the point (4,-5) is 5 units directly below (4,0). We can see that (4,-5) is in Quadrant IV because the x-coordinate is positive, and the y-coordinate is negative.<BR>\n" );
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document.write( "[III] Quadrant II<BR>\n" );
document.write( "We can use the distance formula to show that the circle passes through these quadrants. The point (-1,0) is 5 units directly to the left of (4,0). Let's choose an x-coordinate between 0 and -1, say -0.5. We'll use the distance formula to find the y-coordinate of the point that is exactly 5 units from the center, (4,0).<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D=sqrt%28%28x%5Bc%5D-x%29%5E2%2B%28y%5Bc%5D-y%29%5E2%29 ALIGN=MIDDLE  ALT=\"D=sqrt%28%28x%5Bc%5D-x%29%5E2%2B%28y%5Bc%5D-y%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5=sqrt%28%284-%28-0.5%29%29%5E2%2B%280-y%29%5E2%29 ALIGN=MIDDLE  ALT=\"5=sqrt%28%284-%28-0.5%29%29%5E2%2B%280-y%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5=sqrt%28%284.4%29%5E2%2By%5E2%29 ALIGN=MIDDLE  ALT=\"5=sqrt%28%284.4%29%5E2%2By%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5=sqrt%2819.36%2By%5E2%29 ALIGN=MIDDLE  ALT=\"5=sqrt%2819.36%2By%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now, solve for y. Square both sides of the equation.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25=19.36%2By%5E2 ALIGN=MIDDLE  ALT=\"25=19.36%2By%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2=5.64 ALIGN=MIDDLE  ALT=\"y%5E2=5.64\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=sqrt%285.64%29 ALIGN=MIDDLE  ALT=\"y=sqrt%285.64%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The square root of 5.64 is a positive number, about 2.4. We know that the point (-0.5, sqrt(5.64)) is in Quadrant II because the x- and y-coordinates are positive, negative, respectively.<BR>\n" );
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document.write( "Quadrant III<BR>\n" );
document.write( "The point (-0.5,-sqrt(5.64)) is also exactly 5 units from (4,0). Try it in the distance formula above to see that this is the case. This point is in Quadrant III because both coordinates are negative.<BR>\n" );
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document.write( "Hope this helps! Feel free to email if you have questions about the explanation.<BR>\n" );
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document.write( "Ms.Figgy<BR>\n" );
document.write( "math.in.the.vortex@gmail.com </SPAN>\n" );
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