InterviewSolution
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InterviewSolution
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If the lines `a x+2y+1=0,b x+3y+1=0a n dc x+4y+1=0`are concurrent, then `a ,b ,c`are ina. A.P. b. G.P. c. H.P. d. none of these |
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Answer» Correct Answer - False Given lines are `ax+2y+1=0` `bx+3y+1=0` From Eq. (i), on putting `y=(-ax-1)/(2)` in Eq. (ii), we get `bx-(3)/(2)(ax+1)+1=0` `rArr 2bx-3ax-3+2=0` `rArr x(2b-3a)=1rArrx=(1)/(2b-3a)` Now, using `x=(1)/(2b-3a)` in Eq. (i), we get `(a)/(2b-3a)+2y+1=0` `rArr 2y=-[(a+2b-3a)/(2b-3a)]` `rArr 2y=(-(-2b-2a))/(2b-3a)` `rArr y=((a-b))/(2b-3a)` So, the point of intersection is `((1)/(2b-3a),(a-b)/(2b-3a))` Since, this point lies on `cx+4y+1=0`, then `(c)/(2b-3a)+(4(a-b))/(2b-3a)+1=0` `rArr c+4a-4b+2b-3a=0` `rArr -2b+a+c=0rArr2b=a+c` Hence, the given statement is false. |
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