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Find the equation of the set of points P, the sum of whose distances from A (4, 0, 0) and B (– 4, 0, 0) is equal to 10__________________________Spam will be Report, |
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Answer» Answer Let the COORDINATES of P be (x,y,Z). The coordinates of points A and B are (4,0,0) and (−4,0,0) respectively. It is given that PA+PB=10 √(x+4)ᒾ+yᒾ+zᒾ+√(x+4)ᒾ+yᒾ+zᒾ = 10 √(x+4)ᒾ+yᒾ+zᒾ = 10-√(x+4)ᒾ+yᒾ+zᒾ
On squaring both sides, we OBTAIN (x-4)ᒾ+yᒾ+zᒾ = 100+(x+4)ᒾ+yᒾ+zᒾ-20√(x+4)ᒾ+yᒾ+zᒾ xᒾ-8x+16+yᒾ+zᒾ = 100-20√(x+4)ᒾ+yᒾ+zᒾ+xᒾ+8x+16+yᒾ+zᒾ 20√(x+4)ᒾ+yᒾ+zᒾ = 100+16x 5 = √(x+4)ᒾ+yᒾ+zᒾ = (25+4x) On squaring both sides again, we obtain 25(xᒾ+8x+16+yᒾ+zᒾ) = 625+16xᒾ+200x 25xᒾ+200x+400+25yᒾ+25zᒾ = 625+16xᒾ+200x 9xᒾ+25yᒾ+25zᒾ-225 = 0 Thus the required equation is 9xᒾ+25yᒾ+25zᒾ-225 = 0 |
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