document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1179985>Question 1179985</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the x-coordinates of the points P and Q on y = (x − 7)^2 + 3 such that the tangents at P and Q<BR>\n" );
document.write( "have gradients 1 and −1 respectively.\r<BR>\n" );
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document.write( "b: Show that the square formed by the tangents and normals at P and Q has area 1/2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #809568 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=809568\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "I will describe the process for working the problem and let you do most of the actual work....<br><BR>\n" );
document.write( "Draw a rough sketch of the graph -- it is a parabola that opens upward with vertex (7,3).<br><BR>\n" );
document.write( "(1) Find the derivative of the function: dy/dx = 2(x-7)<BR>\n" );
document.write( "(2) Set the derivative equal to 1 and solve the resulting equation to find the x value where the slope is 1; set it to -1 and solve to find the x value where the slope is -1<br><BR>\n" );
document.write( "That answers the first question....<br><BR>\n" );
document.write( "(3) Sketch the tangents at those two points<BR>\n" );
document.write( "(4) Determine the y values at the two points of tangency (they should be the same)<BR>\n" );
document.write( "(5) Determine the point of intersection of the two tangents (it should be on the axis of symmetry of the parabola, where x=7)<BR>\n" );
document.write( "(6) Determine the side length of the square formed by the tangents and the normals at the points of tangency; that side length is the distance from each point of tangency to the intersection of the two tangents<BR>\n" );
document.write( "(7) Square that side length of the square to verify that the area of the square is 1/2<br><BR>\n" );
document.write( "If you need more help, re-post your question showing what work you have done and telling us what it is that is giving you difficulty<br><BR>\n" );
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