Question

If a, b, c are in H.P. then the straight line $\frac{x}{a}+\frac{y}{b}+\frac{1}{c}=0$ always passes through a fixed point, that point is

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

$Since,a,b,careinH.P.,\therefore \frac{1}{a}+\frac{1}{b}+\frac{1}{c}areinA.P.\Rightarrow \frac{1}{a}+\frac{1}{c}=\frac{2}{b}.......\left(1\right)Thegivenlineis\frac{x}{a}+\frac{y}{b}+\frac{1}{c}=0\frac{x}{a}+\frac{y}{b}+(\frac{2}{b}-\frac{1}{a})=0\left[Using\right(1\left)\right]\Rightarrow \frac{1}{a}(x-1)+\frac{1}{b}(y+2)=0\Rightarrow Thegivenlinepassesthroughtthepointofintersectionofx-1=0andy+2=0i.e.(1,-2)whichisafixedpoint.$