Question 132777
The slopes need to have the relation {{{m[1] = - 1/m[2]}}}
where {{{m[1] = 2k - 4}}} 
and {{{m[2] = k + 6}}}
{{{2k - 4 = -(1/(k + 6))}}}
{{{(2k - 4)(k + 6) = -1}}}
{{{2k^2 + 8k - 24 = -1}}}
{{{2k^2 + 8k - 23 = 0}}}
{{{k = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
{{{k = (-8 +- sqrt( 8^2-4*2(-23) ))/(2*2) }}}
{{{k = (-8 +- sqrt( 248 ))/4 }}}
{{{k = -2 +- (sqrt(62))/2}}}