Question

Find the equation of the line whose nearest point to the origin is $(3,-4)$.

Answer 1

Let line be $AB$

and $P\equiv (3,-4)$

and $O$ being origin

Noe, since $OP\perp AB$,

and slope of $OP=\frac{-4-0}{3-0}=\frac{-4}{3}$

so, slope of $AB=\frac{3}{4}$

so, equation of $AB$ line be

$(y-(-4\left)\right)=\frac{3}{4}(x-3)$

$4y+16=3x-9$

$4y=3x-25$

or $3x-4y-25=0$