Question 1011570
You have the given point J( 10, -8 ). The signs ( +, - )
tell you it is in the 4th quadrant. 
The other point K looks like ( x, 1 )
------------------------------
If you used J as a center and made part of a circle with
radius = 15 in the 2nd quadrant, it crosses the line 
{{{ y = 1 }}} and that is point K
----------------------------
{{{ 15^2 = ( 10 - x[1] )^2 + ( -8 - 1 )^2 }}}
{{{ 225 = 100 - 20x[1] + x[1]^2  + 81 }}}
{{{ x[1]^2 - 20x[1] + 181 - 225 = 0 }}}
{{{ x[1]^2 - 20x[1] - 44 = 0 }}}
I notice that {{{ 44 = 2*22 }}} so I can guess:
{{{ ( x[1] - 22 )*( x[1] + 2 ) = 0 }}}
{{{ x[1] = 22 }}} doesn't work -it's in the 1st quadrant
{{{ x[1] = -2 }}} gives me signs ( -, + ), which is 2nd quadrant
so that works
Point K is ( -2, 1 )
------------------
check answer:
{{{ 15^2 = ( 10 - x[1] )^2 + ( -8 - 1 )^2 }}}
{{{ 15^2 = ( 10 - (-2) )^2 + ( -8 - 1 )^2 }}}
{{{ 15^2 = 12^2 + (-9)^2 }}}
{{{ 225 = 144 + 81 }}}
{{{ 225 = 225 }}}
OK