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 (x1, y1) and (x2, y2);
d = 
By given condition,
Distance of PQ = 
(PQ)2 = 4 × 5
(x – 7)2 + (0 + 4)2 = 20
x2 + 49 - 14x + 16 = 20
x2 - 14x + 65 - 20 = 0
x2 - 14x + 45 = 0
x2 - 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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