How to find the value of ‘a’ and ‘b’ for which the lines given by ax-2y-1=0 , 6x-4y-b=0. a) are parallel b) have no common point ?

1 Answer
Shwetank Mauria
Dec 31, 2017

#a=3# and #b!=2#

Explanation:

When two lines are parallel, they do not have any common point. Hence answer to (a) and (b) are same.

The two lines are parallel when their slopes are equal. The slope of a line can be found by converting its equation to slope intercept form, which is #y=mx+c#, where #m# the coefficient of #x# is the slope of the line and #c# is its intercept on #y#-axis.

For two lines to be parallel their slopes should be equal, but #y#-intercepts should be different i.e. not equal. If #y#-intercepts are equal along with slopes, it makes them coincide i.e. yje two lines are the same.

As #ax-2y-1=0# can be written as #2y=ax-1# or #y=a/2x-1/2#, its slope is #a/2# and #y#-intercept is #-1/2#.

and we can write #6x-4y-b=0# as #4y=6x-b# or #y=6/4x-b/4# i.e, #y=3/2x-b/4#, its slope is #3/2# and #y#-intercept is #-b/4#.

Hence for the two lines to be parallel, we must have

(i) #a/2=3/2# or #a=3#

and (ii) #-b/4!=-1/2# or #b!=2#

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