document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=294471>Question 294471</A>: <I><SPAN STYLE=\"word-break: break-all;\"> explain why radius squared divided by y1 is the y-intercept in the equation of the line tangent to the circle x^2+y^2=r^2\r<BR>\n" );
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document.write( "like in this example: x^2+y^2=17 and the circle meets the tangent at (1,4).What is the equation of the tangent line. The answer is y=(-1/4)x+(17/4)\r<BR>\n" );
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document.write( "Why does the (17/4) equal the radius squard by y1? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #212349 by </B><A HREF=/tutors/aboutme.mpl?userid=scott8148><B>scott8148(6628)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=scott8148><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=scott8148><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=212349\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> it works, in this case, because the circle is centered at the origin\r<BR>\n" );
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document.write( "since the center is at the origin, the slope of a radius to any point (x,y) on the circle is y/x\r<BR>\n" );
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document.write( "a tangent is perpendicular to the radius at the point of tangency, so the slope of the tangent is -x/y\r<BR>\n" );
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document.write( "substituting, the equation for the tangent is ___ y = (-x/y)x + k\r<BR>\n" );
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document.write( "multiplying by y ___ y^2 = (-x)x + (ky) ___ y^2 = -x^2 + (ky)\r<BR>\n" );
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document.write( "adding x^2 ___ y^2 + x^2 = ky\r<BR>\n" );
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document.write( "dividing by y ___ (y^2 + x^2) / y = k ___ r^2 / y = k </SPAN>\n" );
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