12. Find points on the x-axis, each of which is at a
distance of 10 units from the point A(11, - 8).
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Answer:
So, the points are: (17,0) and (5,0).
Explanation:
Let the points on x-axis be P(x,0) and Q(y,0) which are at distance of 10 units from point A(11,−8)
Which implies:
PA=QA
or PA
2
=QA
2
(11−x
1
)
2
+(−8)
2
=(11−x
2
)
2
+(−8)
2
=10
2
(11−x)
2
+(−8)
2
=10
2
121=22x+x
2
+64=100
x
2
−22x+85=0
x
2
−12x−5x+85=0
x(x−17)−5(x−17)=0
(x−17)(x−5)=0
Either (x−17)=0 or (x−5)=0
x=17 or x=5
So, the points are: (17,0) and (5,0).
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