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Question
If points (a, 0), (0, b) and (1, 1) are collinear, then \[\frac{1}{a} + \frac{1}{b} =\]
Options
1
2
0
-1
Solution
We have three collinear points A(a,0) ; B ( 0 , b ) ; C (1 , 1 ) .
In general if `A(x_1,y_1) ;B(x_2 ,y_2) ;C(x_3 ,y_3)` are collinear then,
`x_1 (y_2 -y_3) + x_2 (y_3 - y_1) + x_3 (y_1 - y_2) = 0`
So,
a(b- 1 )+ 0 (1 - 0) + 1(0 - b) = 0
So,
ab = a + b
Divide both the sides by (ab) ,
`1/a + 1/b = 1`
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