Question

If $(a,0),(0,b)$ and $(1,1)$ are collinear, then $\frac{1}{a}+\frac{1}{b}=?$

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

The correct option is A $1$

Let A (0,0), B (0,b) & C(1,1) be the given points

If all the given points are collier

now Area of $△ABC=0$

$\Rightarrow \frac{1}{2}\left|x_1\right(y_2-y_3)+(y_3-y_1)x_2+x_3(y_1-y_2\left)\right|=0$

$\Rightarrow \frac{1}{2}\left|a\right(b-1)+0(1-0)+1(0-b\left)\right|=0$

$\Rightarrow \frac{1}{2}|ab-a-b|=0$

$ab-a-b=0$

$a+b=ab$

$\frac{a}{ab}+\frac{b}{ab}=1$

$\frac{1}{a}+\frac{1}{b}=1$