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If aa n db are two arbitrary constants, ...

If `aa n db` 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.

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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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Knowledge Check

  • If non-zero numbers a, b, c are in H.P., then the straight line (x)/(a)+(y)/(b)+(1)/(c)=0 always passes through a fixed point. That point is

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    A
    `((2)/(5), (2)/(5))`
    B
    `((3)/(5), (3)/(5))`
    C
    `((1)/(5), (1)/(5))`
    D
    `((2)/(5), (3)/(5))`

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