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The length of the straight line x-3y=1 i...

The length of the straight line `x-3y=1` intercepted by the hyperbola `x^2-4y^2=1` is `6/(sqrt(5))` b. `3sqrt(2/5)` c. `6sqrt(2/5)` d. none of these

A

`3/5 sqrt10`

B

`6/5 sqrt10`

C

`5/3 sqrt(10)`

D

`5/6 sqrt(10`

Text Solution

Verified by Experts

The correct Answer is:
B
The Intersection points of given curves are (1,0) and ` (- 13/5, -6/5) `
The distance between these two points
` sqrt((1+13/5)^(2) + (0 + 6/5)^(2)) = 1/5 sqrt(324=36)`
` = 6/5 sqrt10`
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