Derive the equation of the locus of a point twice as far from (-2,3,4) as from (3,-1,-2).

Engineering

Mathematics

Line of Greatest Slope

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(h, k, l) 2 \sqrt{(h + 2)^{2} + (k - 3)^{2} + (l - 4)^{2}} = \sqrt{(h - 3)^{2} + (k + 1)^{2} + (l + 2)^{2}} \Rightarrow 4 (h^{2} + 4 + 4 h + k^{2} + 9 - 6 k + l^{2} + 16 - 8 l) = (h^{2} + k^{2} + l^{2} + 9 + 1 + 4 - 6 h + 2 k + 4 l) \Rightarrow 3 h^{2} + 3 k^{2} + 3 l^{2} + 22 h - 26 k - 36 l + 102 = 0 \Rightarrow 3 x^{2} + 3 y^{2} + 3 z^{2} + 22 x - 26 y - 36 z + 102 = 0

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