If non zero numbers a, b, c are in H.P., then the straight line [x a + y b + 1 c = 0] alwa…

Question

If non zero numbers $a, b, c$ are in $H.P.,$ then the straight line $${x \over a} + {y \over b} + {1 \over c} = 0$$ always passes through a fixed point. That point is :

Accepted Answer

$a,b,c$ are in $$H.P. \Rightarrow {1 \over a}.{1 \over b},{1 \over c}$$ are in $A.P.$

$$ \Rightarrow {2 \over b} = {1 \over a} + {1 \over c}$$

$$ \Rightarrow {1 \over a} - {2 \over b} + {1 \over c} = 0$$

$$\therefore$$ $${x \over a} + {y \over a} + {1 \over c} = 0$$ passes through $$\left( {1, - 2} \right)$$

Solutions · 1