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Distance between the pair of lines repre...

Distance between the pair of lines represented by the equation `x^(2)-6xy+9y^(2)+3x-9y-4=0`, is

A

`(15)/(sqrt(10))`

B

`(1)/(2)`

C

`sqrt((5)/(2))`

D

`(1)/(sqrt(10))`

Text Solution

Verified by Experts

The correct Answer is:
C
The distance between the pair of straight lines given by
`ax^(2)+2hxyt+by^(2)+2gx+2fy+c=0`
is `=2sqrt((g^(2)-ac)/(a(a+b)))`
Here, a=1,b=9,c=-4,g=`(3)/(2)`
Required distance
`=2sqrt((9//4)-(-4))/(1(1+9)))`
`=2sqrt((25//4)/(10))=sqrt((5)/(2))`
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Knowledge Check

  • The distance between the pair of lines represented by the equation x^(2)-6xy +9y^(2)+3y-9y-4=0 is

    A
    `(15)/(sqrt(10))`
    B
    `(1)/(2)`
    C
    `sqrt((5)/(2))`
    D
    `(1)/(sqrt(10))`

  • The distance between the pair of parallel lines represented by the equation x^2-6xy+9y^2+3x-9y-4=0 is

    A
    `(15)/(sqrt10)`
    B
    `1/2`
    C
    `sqrt(5/2)`
    D
    `1/(sqrt(10))`

  • The nature of straight lines represented by the equation 4x^(2)+12xy+9y^(2)=0 is

    A
    Real and coincident
    B
    Real and different
    C
    Imaginary and different
    D
    None of the above

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