Question

Find the point on x-axis which is equidistant from the points (2,-2) and (-4,2)
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Answer 1

ANSWER :

Let the other two point be A(−2,5) and B(2,−3)

So by distance formula we have,

Distance between two points =   (x  2   −x  1 ​  )  2  +(y  2 ​−y  1 )  2

 

Then,

PA=PB   PA  2  =PB  2  

⇒(a+2)  2  +(0−5)  2  =(a−2)  2  +(0+3)  2

 ⇒a  2  +4+4a+25=a  2 +4−4a+9

⇒4a+29=−4a+13

⇒ 8a=−16⇒a=−2

∴ The required point is P(−2,0)

Answer 2

Let P(x,0) be a point on X-axis

PA = PB

PA2 = PB2 (x - 2)2 + (0 + 2)2 = (x + 4)2 + (0 - 2)2

x2 + 4 - 4x + 4

= x2 + 16 + 8x + 4

-4x + 4 = 8x + 16

x = -1

P(-1,0)