Math, asked by mohita08, 11 months ago

a.
Find the points on the x-axis whose distances from the points A (7,6) and
B(-3, 4) are in ratio 1:2....pls solve this...i had solved but still not sure of the answer...​

Answers

Answered by amitnrw
12

Points are ( 35/3 , 0)  & ( 9 , 0)

Step-by-step explanation:

Let say point P on the x axis

= ( P , 0)

Distance of P from A  ( 7 , 6)   =  √(P - 7)² + (6 - 0)²

= √(P - 7)² + 6²

= √P²+ 49 - 14P + 36

= √P²- 14P + 85

Distance of P from B  ( -3 , 4)   =  √(P - (-3))² + (4 - 0)²

=  √(P + 3)² + 4²

= √P²+ 9 +6P + 16

= √P² + 6P + 25

PA/PB  = 1/2

=> √P²- 14P + 85 / √P² + 6P + 25   = 1/2

Squaring both sides

=> (P²- 14P + 85) / (P² + 6P + 25 )  = 1/4

=> 4P² - 56P + 340 = P² + 6P + 25

=> 3P² - 62P  + 315 = 0

=> 3P² - 27P - 35P  + 315 = 0

=> 3P(P - 9) - 35(P - 9) = 0

=> (3P - 35) (P - 9) = 0

=> P = 35/3  , P = 9

Points are ( 35/3 , 0)  & ( 9 , 0)

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