Question

find the points on the x-axis each of which is at a distance of 5 units from the pount a(5,-3)

Answer 1

Answer :

Let us take the point on x axis be (x, 0)

By the given condition,

$\sqrt{ {(x - 5)}^{2} + {(0 + 3)}^{2} } = 5 \\ \\ \implies \sqrt{ {(x - 5)}^{2} + 9} = 5 \\ \\ \implies {(x - 5)}^{2} + 9 = {5}^{2} = 25 \\ \\ \implies {(x - 5)}^{2} = 25 - 9 = 16 = {4}^{2}$

$\implies$ (x - 5) = ± 4

$\implies x = 9 \: \: or \: \: x = 1$

Therefore, the points on x - axis are having co-ordinates (9, 0) and (1, 0).

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