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The point of concurrence of the line ax+...

The point of concurrence of the line ax+by+c=0 and a,b,c satisfy the relation 3a+2b+4c=0 is

A

(3/2,1/4)

B

(3/4,1/4)

C

(3/4,1/2)

D

(3/2,1/2)

Text Solution

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The correct Answer is:
C
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If a + 2b + 3c = 0 " then " a/3+(2b)/3+c=0 and comparing with line ax + by + c, we get x = 1/3 & y = 2/ 3 so there will be a point (1/3,2/3) from where each of the lines of the form ax + by + c = 0 will pass for the given relation between a,b,c . We can say if there exists a linear relation between a,b,c then the family of straight lines of the form of ax + by +c pass through a fixed point . If a , b,c are in A.P., then the line ax + 2by + c = 0 passes through

If a + 2b + 3c = 0 " then " a/3+(2b)/3+c=0 and comparing with line ax + by + c, we get x = 1/3 & y = 2/ 3 so there will be a point (1/3,2/3) from where each of the lines of the form ax + by + c = 0 will pass for the given relation between a,b,c . We can say if there exists a linear relation between a,b,c then the family of straight lines of the form of ax + by +c pass through a fixed point . If a , b, c are consecutive odd integers then the line ax + by + c = 0 will pass through