Question 935410
The ratio uses the distance between the given points in five equal parts, and you want {{{2/5}}} of this distance from one point to the other point.


Distance Formula!  Unknown point between, (x,y).


Distance between given points, {{{sqrt((-2-(-4))^2+(6-(-5))^2)}}},
{{{sqrt(4+121)}}}
{{{sqrt(125)}}}
{{{highlight_green(5sqrt(5))}}}


Another way to take the rest of this is from (-5,-4) to (x,y) is 2 parts and from (x,y) to (6,-2) is 3 parts.  Still two equations are needed.


---
{{{sqrt((x-(-5))^2+(y-(-4))^2)=(2/5)5*sqrt(5)}}}
{{{sqrt((x+5)^2+(y+4)^2)=2sqrt(5)}}}
{{{highlight_green((x+5)^2+(y+4)^2=20)}}}

AND

{{{sqrt((x-6)^2+(x-(-2))^2)=(3/5)5*sqrt(5)}}}
{{{sqrt((x-6)^2+(y+2)^2)=3*sqrt(5)}}}
{{{highlight_green((x-6)^2+(y+2)^2=45)}}}
---


Instead of continuing to try to solve these two simultaneous quadratic equations in two variables, find and use the equation of the line containing the two given points!!
{{{m=(-2-(-4))/(6-(-5))=2/11}}}
and pick second point,
{{{y=(2/11)x+(-2-(2/11)*6)}}}
{{{y=(2/11)x+(-2-12/11)}}}
{{{y=(2/11)x+(-22/11-12/11)}}}
{{{highlight_green(y=(2/11)x-34/11)}}}


A large number of more arithmetic steps using some substitutions with this line equation.  (unfinished here)