Question

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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

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Answer 1

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

Answer 2

Answer:

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Step-by-step explanation:

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