Straight Line And Pair Of Straight Lines Ques 40

Solution:

Formula:

A Point and Line:

40. Let the variable straight line be $a x+b y+c=0$

where, algebraic sum of perpendiculars from $(2,0),(0,2)$ and $(1,1)$ is zero.

$$ \begin{array}{cc} \therefore & \frac{2 a+0+c}{\sqrt{a^{2}+b^{2}}}+\frac{0+2 b+c}{\sqrt{a^{2}+b^{2}}}+\frac{a+b+2c}{\sqrt{a^{2}+b^{2}}}=0 \\ \Rightarrow & 3a + 3b + 3c = 0 \ \Rightarrow & a+b+c=0 \end{array} $$

From Eqs. (i) and (ii) $a x+b y+c=0$ does not necessarily pass through a fixed point $(1,1)$.