document.write( "Question 947097: please i want you to help me find the equation of the locus of points equidistant from the point(0,2) and the straight line y=4. \n" ); document.write( "

Algebra.Com's Answer #797678 by ikleyn(52787) $\"\"$ $\"About$

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document.write( "Let (x,y) be the point of the locus.\r\n" );
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document.write( "Then the distance to the point (0,2) is\r\n" );
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document.write( "    d =  = .\r\n" );
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document.write( "while the distance to the straight line y= 4 is  |y-4|.\r\n" );
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document.write( "Two distances are the same; it gives an equation\r\n" );
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document.write( "     = |y-4|.\r\n" );
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document.write( "Square both sides\r\n" );
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document.write( "    x^2 + y^2 - 4y + 4 = y^2 - 8y + 16.\r\n" );
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document.write( "Simplify\r\n" );
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document.write( "    x^2 = - 4y + 12,   or\r\n" );
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document.write( "    4y  = - x^2 + 12,  or\r\n" );
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document.write( "     y  = - .\r\n" );
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document.write( "It is the parabola opened downward, with the symmetry axis x= 0, \r\n" );
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document.write( "with the vertex at the point  (0,3) and x-intercepts at x= -   and  x= .\r\n" );
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document.write( "    \r\n" );
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document.write( "    Plot y = - (red) and y = 4 (green)\r\n" );
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