Find the points on the X - axis which are at a distance of from the point (7, - 4). How many such points are there?

We know that, every point on the X - axis in the form (x, 0).

Let P(x, 0) the point on the X - axis have distance from the point Q(7, - 4).

As we know;

Distance between the points (x_{1}, y_{1}) and (x_{2}, y_{2});

d =

By given condition,

Distance of PQ =

(PQ)^{2} = 4 × 5

(x – 7)^{2} + (0 + 4)^{2} = 20

x^{2} + 49 - 14x + 16 = 20

x^{2} - 14x + 65 - 20 = 0

x^{2} - 14x + 45 = 0

x^{2} - 9x – 5x + 45 = 0

By Factorization method:

x(x - 9) – 5(x – 9) = 0

(x – 9)(x – 5) = 0

∴ x = 5, 9

Hence, there are two points lies on the axis, which are (5, 0) and (9, 0), have distance from the point (7, - 4).

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