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

The equations of a line which is parallel to the line common to the pa

1.	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 iosA. `3x-4y=-35`B. `5x-2y=7`C. `3x+4y=35`D. `2x-3y=7`
Answer» Correct Answer - 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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