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The equation of a line which is parallel...

The equation of a line which is parallel to the line common to the pair of lines given by `6x^2-x y-12 y^2=0` and `15 x^2+14 x y-8y^2=0` and at a distance of 7 units from it is
(a)`3x-4y=-35`
(b) `5x-2y=7`
(c) `3x+4y=35`
(d)`2x-3y=7`

A

`3x-4y=-35`

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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