Question 1094343
Let the point on the x-axis be ( x[1], 0 )
Use distance formula to find distance
from ( -3,5 )
{{{ 13^2 = ( x[1] -(-3) )^2 + ( 0 - 5 )^2 }}}
{{{ 169 = ( x[1] + 3 )^2 + 25 }}}
{{{ ( x[1] + 3 )^2 = 12^2 }}}
Take the square root of both sides
{{{ x[1] + 3 = 12 }}}
{{{ x[1] = 9 }}}
and, taking negative square root,
{{{ x[1] + 3 = -12 }}}
{{{ x[1] = -15 }}}
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The possible points for P are:
( 9, 0 ) and
( -15,0 )
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check:
{{{ ( x[1] + 3 )^2 = 144 }}}
{{{ ( -15 + 3 )^2 = 144 }}}
{{{ 12^2 = 144 }}} 
OK
and
{{{ ( 9 + 3 )^2 = 144 }}}
{{{ 12^2 = 144 }}}
OK