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If a , b ,c are in harmonic progression,...

If `a , b ,c` are in harmonic progression, then the straight line `(x/a)+(y/b)+(1/c)=0` always passes through a fixed point. Find that point.

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a,b,c are in HP. Then,
`(2)/(b) = (1)/(a) + (1)/(c)" "(1)`
The given line is
`(x)/(a) + (y)/(b) + (1)/(c) = 0" "(2)`
Subtracting (1) from (2), we get
`(1)/(a)(x-1) + (1)/(b)(y+2) =0`
Since `a ne 0 " and " b ne 0`, we get
x-1 =0 and y+2 = 20
or x =1 and y=-2
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