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Question

Find the equations of lines with slope 2 and length of perpendicular distance from origin is equal to 3 units.

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Solution

The equation of the family of lines with slope 2 is y=2x+c
or 2xyc=0 .......(1)
For the required members of the family, the perpendicular distance from the origin (0,0) is 3 units.
|2×00c|(2)2+(1)2=3
|c|4+1=6
c=±30=±30
the equations of the lines are 2xy+30=0 or 2xy30=0

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