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Question

Equation of a line which is parallel to the line common to the pair of lines given by 6x2xy12y2=0 and 15x2+14xy8y2=0 and at a distance of 7 units from it, is

A
3x+4y=35
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B
3x+4y+35=0
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C
2x3y=35
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D
2x3y+35=0
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Solution

The correct option is B 3x+4y+35=0
We have, 6x2xy12y2=0
(2x3y)(3x+4y)=0 (1)
and 15x2+14xy8y2=0
(5x2y)(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 units,
so ∣ ∣k32+42∣ ∣=7
k=±35

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