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The equations of a line which is paralle...

The equations of a line which is parallel to the line common to the pair of lines given by `6x^(2)-xy-12y^(2)=0and15x^(2)+14xy-8y^(2)=0`and the sum of whose intercepts on the axes is 7, is :

A

`3x+4y=12`

B

`5x-2y=7`

C

`3x+4y=35`

D

`2x-3y=7`

Text Solution

Verified by Experts

The correct Answer is:
3
We have `6x^(2)-xy-12y^(2)=0`
or `(2x-3y)(3x+4y)=0` (1)
and `15x^(2)+14xy-8y^(2)=0`
or `(5x-2y)(3x+4y)=0` (2) Equation of the line common to (1) and(2) is
`3x+4y=0` (3)
Equation of any line parallel to (3) is
`3x+4y=k`
Since its distance from (3) is 7 ,we have
`|(k)/(sqrt(3^(2)+4^(2)))|=7ork=+-35`
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Knowledge Check

  • The equations of a line parallel to the line 3 x + 4y = 0 and touching the circle x^(2) + y^(2) = 9 in the 1st quardrant is

    A
    `3x + 4y = 15`
    B
    `3x + 4y = 45`
    C
    `3x + 4y = 0 `
    D
    `3x + 4y = 27 `

  • Type of quadrilateral formed by the two pairs of lines 6x^2-5xy-6Y^2=0 and 6x^2-5xy-6Y^2+x+5y-1=0 is

    A
    square
    B
    rhombus
    C
    parallelogram
    D
    rectangle

  • The equation of the tangent to the parabola y^(2) = 4x + 5 which is parallel to the line y= 2x + 7 is-

    A
    `y= 2x -3`
    B
    `y=2x+3`
    C
    `y= 2x-5`
    D
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