Question 1188642
A line passes through A(2,-2) and B(-4,3). Find the coordinates of the point on the line twice as far from A as from B (show two cases).
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(x,y) is a point twice as far from A as from B
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Distance from A = {{{sqrt((x-2)^2 + (y+2)^2)}}}
Distance from B = {{{sqrt((x+4)^2 + (y-3)^2)}}}
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{{{sqrt((x-2)^2 + (y+2)^2) = 2*sqrt((x+4)^2 + (y-3)^2)}}}
{{{(x-2)^2 + (y+2)^2 = 4*((x+4)^2 + (y-3)^2)}}}
{{{x^2 - 2x + 4 + y^2 + 2y + 4 = 4x^2 + 32x + 64 + y^2 - 6y + 9}}}
{{{-3x^2 - 34x - 60 + 8y - 5 = 0}}}
{{{3x^2 + 34x + 65 = 8y}}}
{{{y = (3/8)x^2 + (17/4)x + 65/8}}}
At x = 0, y = 65/8 ---> (0,65/8)
At x = -2, y = 9/8 --> (-2,1.125)