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A line 2x + y = 1 intersect co-ordinate ...

A line `2x + y = 1` intersect co-ordinate axis at points `A` and `B`. A circle is drawn passing through origin and point `A` & `B`. If perpendicular from point `A` and `B` are drawn on tangent to the circle at origin then sum of perpendicular distance is (A) `5/sqrt2` (B) `sqrt5/2` (C) `sqrt5/4` (D) `5/2`

A

`2sqrt5`

B

`sqrt5/2`

C

`4sqrt5`

D

`sqrt5/4`

Text Solution

Verified by Experts

The correct Answer is:
B
A(1,0), `B(0,1/2)` and O(0,0)
AB is diameter of the circle so equation is (x-1)(x-0)+(y-0)`(y-1/2)=0`
`rArr x^2+y^2-x-1/2y=0`
Equation of tangent at O(0,0) is given by T=0 `rArr` 2x+y=0
Sum of `bot` distances from A and B to tangents is `=2/sqrt5+(1/2)/sqrt5=5/(2sqrt5)=sqrt5/2`
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