The tangents to the curve xy=6at P(2,3) meets the coordinate axes at A and B. The ratio in which P divides AB IS
Answer (1)
28th May, 2020
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Given equation of curve = xy=6at
p=(2.,3)
O=(0,0)
slope m= 3/2
OP is Perpendicular to AB
therefore m=-2/3
From,y=mx+c
where m=-2/3 & P=(2,3)
by substituting ,3=-4/3+c
c=13/3
by solving we get y=13/3 and x=13/2
Let A=(0,y) and B=(x,0)
AB is divided by P in the ratio λ : 1
therefore
(2,3)= λ (13/2) / λ +1 ,, 13/3 / λ +1
By equating,,
2=λ (13/2) / λ +1 3=13/3 / λ +1
on solving we get λ=4/9
The ratio in which P divides AB in the ratio 4:9
Hope it helps!!!
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