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A straight line passing through the point`(2,2)` and the axes enclose an area `lamda`. The intercepts on the axes made by the line are given by the two roots of:
(A)   `x^2-2|lamda|x+|lamda|=0`   (B)   `x^2+|lamda|x+2|lamda|=0`
(C)   `x^2-|lamda|x+|2lamda|=0`   (D)   None of these

A

`x^(2_-2lamdax+lamda=0`

B

`x^(2)+lamdax+2lamda=0`

C

`x^(2)-lamdax+2lamda=0`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
Let the equation off line is
`(x)/(a)+(y)/(b)=1`
it passes through (2,2)
So, `(2)/(a)+(2)/(b)=1` . . . (i)
and `(1)/(2)ab=lamda`
`ab=2lamda` (given) . . . (ii)
`therefore` From Eq. (i), we get
`(2(a+b))/(ab)=1 impliesa+b=(ab)/(2)`
`impliesa+b=lamda` [from Eq. (ii)]
Hence, required equation is
`x^(2)-lamdax+2lamda=0`
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