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find the equation of the circle with center at y-axis and which passes through the origin and the point (4,2)
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\n" ); document.write( "The line thru the origin and (4,2) is a chord of the circle. So the perpendicular bisector of it will go thru the center. The intersection of that line and the y-axis will be the center of the circle.
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\n" ); document.write( "Find the eqn of the line thru (0,0) and (4,2).
\n" ); document.write( "m = diffy/diffx = 2/4
\n" ); document.write( "m = 1/2 (the slope)
\n" ); document.write( "The midpoint of the line is (2,1) (see that?)
\n" ); document.write( "The slope of the line perpendicular will be the negative inverse, = -2
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\n" ); document.write( "Find the eqn of the line with a slope of -2 thru (2,1)
\n" ); document.write( "y-y1 = m*(x-x1)
\n" ); document.write( "y-1 = -2*(x-2)
\n" ); document.write( "y-1 = -2x+4
\n" ); document.write( "y = -2x+5
\n" ); document.write( "The y-intercept is 5, so the point (0,5) is the center of the circle (it was stated to be on the y-axis).
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\n" ); document.write( "Since the circle also goes thru the origin, the radius is 5.
\n" ); document.write( "x^2 + (y-5)^2 = 25 is the circle
\n" ); document.write( "or
\n" ); document.write( "x^2 + y^2 - 10y + 25 = 25
\n" ); document.write( "x^2 + y^2 - 10y = 0 \n" ); document.write( "