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Question

Equation of a line which is parallel to the line common to the pair of lines given by 6x2xy12y20 and 15x2+14xy8y20 and at a distance 7 from it is


A

3x+4y=35

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B

5x2y=7

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C

3x+4y=35

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D

2x3y=7

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Solution

The correct options are
A

3x+4y=35


C

3x+4y=35


6x2xy12y2=0
(2x - 3y)(3x + 4y) = 0 (i)
and 15x2 + 14xy - 8y2 = 0
(5x - 2y) (3x + 4y) = 0 (ii)
Equation of the line common to (i) and (ii) is
3x + 4y = 0 (iii)
Equation of any line parallel to (ii) is
3x + 4y = k
Since its distance from (iii) is 7
k32+42=7k=±(7×5)=±35


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