find the co ordi a5es of the points on the x axis which are at a distance of 5 units from the point (6,-3)
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Answer:
Any point on X-axis has co-ordinates of form (x,0)
∴(x
1
,y
1
)=(6,−3) and (x
2
,y
2
)=(x,0) and d=5
∴d=
(x
2
−x
1
)
2
+(y
2
−y
1
)
2
5=
(x−6)
2
+[0−(−3)]
2
=
(x−6)
2
+3
2
Squaring on both sides 5
2
(
(x−6)
2
+9
)
2
25=x
2
−12x+36+9
x
2
−12x+45−25=0⇒x
2
−12x+20=0⇒(x−10)(x−2)=0
∴x−10=0 or x−2=0⇒x=10 or x=2
∴ Required points on X-axis are (10,0) and (2,0)
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