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Prove that all the lines having the sum ...

Prove that all the lines having the sum of the interceps on the axes equal to half of the product of the intercepts pass through the point. Find the fixed point.

A

`(1, 1)`

B

`(2, 2)`

C

`(3, 3)`

D

`(4, 4)`

Text Solution

Verified by Experts

The correct Answer is:
B
Let a and b the intercepts made by the straight line on the axes. Then, according to question
`a+b=(ab)/(2)" "rArr" "(2)/(a)+(2)/(b)=1`
`"On comparing with "(x)/(a)+(y)/(b)=1" we get "rArr" "x=2, y=2`
Hence, straight passes through the point `(2, 2)`
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