Question 1080804
y=2x, perpendicular line going through Origin
Points  (x, 2x).


{{{(x-0)^2+(2x-0)^2=2^2}}}
{{{x^2+4x^2=4}}}
{{{5x^2=4}}}
{{{x=0+- sqrt((4/5))}}}

{{{x=0+- 2/sqrt(5)}}}


{{{y=-4/sqrt(5)}}}
{{{y=-4*sqrt(5)/5}}}
OR
{{{y=4*sqrt(5)/5}}}


Line wanted
slope must be  {{{-1/2}}} and either contain  (-2*sqrt(5)/5, -4*sqrt(5)/5 )  or  ( 2*sqrt(5)/5, 4*sqrt(5)/5 ).
ONE of the lines:   {{{highlight_green(y-4*sqrt(5)/5=-(1/2)(x-2*sqrt(5)/5))}}}; you can simplify this, and form the other line...