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Question 2
Find the points on the X-axis which are at a distance of 25 from the point (7, -4). How many such points are there?

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Solution

We know that, every point on the X-axis in the form (x,0).
Let the point on the X-axis be P(x,0) .
Given: P(x,0) is at a distance of 25 units from the point Q(7,-4).
By given condition,PQ=25
[Distance formula(x2x1)2+(y2y1)2]
(PQ)2=4×5(x7)2+(0+4)2=20x2+4914x+16=20x214x+6520=0x214x+45=0x29x5x+45=0[by factorisation method]x(x9)5(x9)=0(x9)(x5)=0x=5 and 9
Hence, there are two such points i.e., point P can be (5,0) or (9,0).
[ Both the points are at a distance of 25 from (7, -4) ]

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