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 at a distance of 7 units from it ios

Options

A. `3x-4y=-35`
B. `5x-2y=7`
C. `3x+4y=35`
D. `2x-3y=7`

Answer

3

Explanation

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`