Just did a specific one of these; let's do the general case.
The point nearest the origin is (a,b).
The line from the origin through the point is
[tex]bx - ay = 0[/tex]
The line we seek is perpendicular to this one. We swap the coefficients on x and y, negating one, to get the perpendicular family of lines. We set the constant by plugging in the point (a,b):
[tex]ax + by = a^2 + b^2[/tex]
[tex]ax + by -( a^2 + b^2) = 0[/tex]
That's standard form; let's plug in the numbers:
[tex]4 x - 4 y - 32 = 0 [/tex]
[tex] x - y - 8 = 0[/tex]
