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if non-zero numbers a,b,c are in HP then the st. line x/a + y/b + 1/c=0 always passes trough the fixed point:-

1) (-1,-2)

2) (-1,2)

3) (1,-1/2)

4) (1,-2)

$\frac{1}{a}+\frac{1}{c}=\frac{2}{b}\phantom{\rule{0ex}{0ex}}\Rightarrow \frac{1}{a}-\frac{2}{b}+\frac{1}{c}=0\phantom{\rule{0ex}{0ex}}thereforetheline\frac{x}{a}+\frac{y}{b}+\frac{1}{c}=0\phantom{\rule{0ex}{0ex}}passesthroughthepoint(1,-2)\phantom{\rule{0ex}{0ex}}thusoption\left(4\right)iscorrect$

hope this helps you

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