What is the locus of points equidistant from the lines ax + by + c = 0?
A line bx - ay +q = 0
A line ax - by +q = 0
A line bx + ay +q = 0
A line ax + by +q = 0
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There is no correct option, the answer is ay - bx + ø = 0, which is not among the options given.
The locus of points equidistant from a given line \( ax + by + c = 0 \) is actually a pair of parallel lines. These lines will be parallel to the given line and equidistant on either side.
The equation of a line parallel to \( ax + by + c = 0 \) will have the same coefficients for \( x \) and \( y \), but a different constant.
Thus, the equation for a line parallel to the given line can be expressed as \( ax + by + q = 0 \), where \( q \) is some constant different from \( c \).
So, the correct answer is D. A line \( ax + by + q = 0 \).
The answer is not there, even the answer you solved in the solution is not in the options, please review this question.
