document.write( "Question 1191710: Derive the equation of the locus of a point P(x,y) which moves so that its distance from (2,3) is always equal to its distance from the line x+2=0 \n" ); document.write( "

Algebra.Com's Answer #823535 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "You don't need to use the \"equal distance\" information to write and simplify an equation that says the distance from the point is equal to the distance from the line.

\n" ); document.write( "The given information defines a parabola with directrix x=-2 and focus (2,3).

\n" ); document.write( "With directrix x=-2 and focus (2,3), the vertex is (0,3). The parabola opens to the right; the equation in vertex form is

\n" ); document.write( " $\"x-h=%281%2F%284p%29%29%28y-k%29%5E2%29\"$

\n" ); document.write( "where (h,k) is the vertex and p is the directed distance (i.e., could be negative) from the vertex to the focus.

\n" ); document.write( "In this problem, (h,k) is (0,3) and p is 2. So the equation is

\n" ); document.write( " $\"x-0=%281%2F8%29%28y-3%29%5E2\"$

\n" ); document.write( "or

\n" ); document.write( " $\"x=%281%2F8%29%28y-3%29%5E2\"$

\n" ); document.write( "or

\n" ); document.write( " $\"8x=%28y-3%29%5E2\"$

\n" ); document.write( " \n" ); document.write( "

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