If a and b are two arbitrary constants, ...

If `a and b` are two arbitrary constants, then prove that the straight line `(a-2b)x+(a+3b)y+3a+4b=0` will pass through a fixed point. Find that point.

Text Solution

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(a-2b)x+(a+3b)y+3a+4b=0
or a(x+y+3)+b(-2x+3y+4)=0
which represents a family of straight lines passing through the point of intersection of x+y+3=0 and -2x+3y+4 = 0, i.e., (-1,-2).

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