1.

Find those points on x -axis, each of which is at a distance of 5 units from the point A(5, -3)`

Answer» Let the required point on the x-axis be P(x, 0). Then,
`PA = 5 rArr PA^(2) = 25`
`rArr (x-5)^(2) + (0 +3)^(2) = 25`
`x^(2) -10x +25 +9 =25 rArr x^(2) - 10x +9 =0`
`x^(2) -x -9x +9 =0 rArr x(x-1) -9 (x-1) =0`
`rArr (x-1) (x-9) = 0 rArr x - 1 =0 "or" x - 9=0`
`rArr ` x = 1 or x = 9
Hence, the required points on the x-axis are B(1, 0) and C(9, 0).


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