document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=264572>Question 264572</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the circle, centre (p,q) radius 25, meets the x axis at (-7,0) and (7,0) where q>o.<BR>\n" );
document.write( "find the value of p and q<BR>\n" );
document.write( "find the coordinates of the points where the circle meets the y axis<BR>\n" );
document.write( "THANK YOU SO MUCH IF YOU CAN HELP!! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #194794 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=194794\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> formula for the circle is (x-p)^2 + (y-q)^2 = 25^2\r<BR>\n" );
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document.write( "this is from the standard formula of (x-h)^2 + (y-k)^2 = r^2 where (h,k) is the center of the circle, and r^2 is the square of the radius of the circle.\r<BR>\n" );
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document.write( "the center of your circle is (p,q), so we have h = p and q = k.\r<BR>\n" );
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document.write( "the radius of your circle is 25, which makes the equation:\r<BR>\n" );
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document.write( "(x-p)^2 + (y-q)^2 = 25^2\r<BR>\n" );
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document.write( "we know that (0,-7) is on the circle and (0,7) is on the circle.\r<BR>\n" );
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document.write( "we know that from the center of the circle to (0,-7), the length is 25.\r<BR>\n" );
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document.write( "we know that from the center of the circle to (0,7), the length is 25.\r<BR>\n" );
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document.write( "if we call the center of the circle A, and the point (0,-7) B, and the point (0,7) C, then we have an isosceles triangle whose sides are each 25 units in length and whose base is 14 units in length is sqrt (-7-7)^2 + (0-0)^2) = sqrt(14^2) = 14.\r<BR>\n" );
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document.write( "if we drop a perpendicular from the center of the circle (point A), perpendicular to the base of the triangle (side BC), then we have something that looks like 2 right triangles, with the x-axis as the base and the y-axis as the altitude.\r<BR>\n" );
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document.write( "we'll call the intersection of the perpendicular to the base point D.\r<BR>\n" );
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document.write( "The 2 right triangles are ABD and ACD.\r<BR>\n" );
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document.write( "side BD is 7 units in length.<BR>\n" );
document.write( "side CD is 7 units in length.<BR>\n" );
document.write( "side AB is 25 units in length.<BR>\n" );
document.write( "side AC is 25 units in length.\r<BR>\n" );
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document.write( "We can find the length of AD by finding the angle ACD.\r<BR>\n" );
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document.write( "Cosine of ACD = adjacent / hypotenuse = CD / AC = 7/25 = .28\r<BR>\n" );
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document.write( "Arc Cosine of .28 = 73.73979529 degrees.\r<BR>\n" );
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document.write( "Tangent of 73.73979529 degrees = opposite / adjacent =  AD / DC = AD / 7\r<BR>\n" );
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document.write( "multiply both sides of this equation by 7 to get:\r<BR>\n" );
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document.write( "7 * Tangent of 73.73979529 degrees = AD.\r<BR>\n" );
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document.write( "This makes AD = 24 units in length.\r<BR>\n" );
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document.write( "Since point A is the center of the circle and is on the y-axis 24 units above the x-axis, this makes the center of the circle equal to (x,y) = (0,24)\r<BR>\n" );
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document.write( "Since the center of the circle is (0,24), then the equation of the circle becomes:\r<BR>\n" );
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document.write( "(x-0)^2 + (y-24)^2 = 25^2\r<BR>\n" );
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document.write( "We can graph this equation by solving for y.\r<BR>\n" );
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document.write( "We solve for y to get y = 24 +/- sqrt(25^2 - x^2))\r<BR>\n" );
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document.write( "graph of that equation is shown below:\r<BR>\n" );
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document.write( "A diagram of what the circle looks like with it's isosceles triangle is shown below:\r<BR>\n" );
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document.write( "The y-axis is the vertical line in the middle.\r<BR>\n" );
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document.write( "The x-axis is the horizontal line at the 0 mark.\r<BR>\n" );
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document.write( "The question was:\r<BR>\n" );
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document.write( "find the value of p and q<BR>\n" );
document.write( "find the coordinates of the points where the circle meets the y axis\r<BR>\n" );
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document.write( "The value of (p,q) = (0,24)\r<BR>\n" );
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document.write( "The points where the circle meets the y-axis are (0,49) and (0,-1)./\r<BR>\n" );
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document.write( "This is found by looking at the graph and solving the following equation.\r<BR>\n" );
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document.write( "The equation is x^2 + (y-24)^2 = 25^2\r<BR>\n" );
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document.write( "when x = 0, the equation becomes (y-24)^2 = 25^2\r<BR>\n" );
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document.write( "take square root of both sides of this equation to get y-24 = +/- 25\r<BR>\n" );
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document.write( "add 24 to both sides of this equation to get y = 24 +/- 25\r<BR>\n" );
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document.write( "24 + 25 = 49\r<BR>\n" );
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document.write( "24 - 25 = -1\r<BR>\n" );
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