Question 785424
Find an equation such that the distance between (x,y) and (3,5) is twice that of (-2,-4)

Interpretation:
Find an equation that describes all the points that are spaced twice the distance between (-2,-4) and (3,5) from (3,5). In other words find a circle with radius of twice the distance between (-2,-4) and (3,5).

Find the distance between (-2,-4) and (3,5):
Using the distance formula {{{distance = sqrt((dx)^2+(dy)^2)}}}
{{{D = sqrt((-2-3)^2+(-4-5)^2)}}}
{{{D = sqrt((-5)^2+(-9)^2)}}}
{{{D = sqrt(106)}}}
Seeing that the points are double the distance away, the radius of the circle is 2d which means the equation describing the points is 
{{{(2D)^2=(x-3)^2+(y-5)^2}}}
{{{ 4D^2=(x-3)^2+(y-5)^2}}}
{{{ (x-3)^2+(y-5)^2 = 424}}}
explaination
any point on this line is twice the distance between(3,5) and (-2,-4) from the centre (3,5)
{{{drawing( 300, 300, -30, 30, -30, 30,
  grid( 1 ),
  circle(3, 5, sqrt(424)),
  circle( 3, 5, 0.2 ),
  locate( 3, 5, "(3,5)" )
)}}}