a parameter is basically any arbitary value.....it can take any value.....it is used to reducing the number of unknowns in an eqn (especially in conix)..... in this sum.......lambda basically means any real number...... if u have a line 2x + 5y = 6 its slope is -2/5 any line parallel to it will have the same slope thus, y = mx + c y = -2/5 x + c 5y = -2x + 5c 2x + 5y = 5c now we can put 5c = lambda (both are constants)
thus in general, if u r given any line and u have to find line parallel to it simply decide its constant term and ur sum is solved
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it represents a "family of lines" parallel to line ax + by + c= 0
now for different values of ... the equation will reperesent different lines of the family... is a parameter... which for different values will give different lines..for every unique value of ....the equation will represent a unique curve(here line)
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Nunoxic has somewat explained on the right track .. lemme try to put some more light. Well see since the slope of all parrallel lines will be same so the coefficients of x and y remain same in all the lines. However there can be infinite lines parrallel to a given line and hence the constant term cannot be unique and it can vary and thus the lamda here is a parameter which can vary .
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