Question

If the points $(a,0),(0,b)$ and $(1,1)$ are collinear, then $\frac{1}{a}+\frac{1}{b}$ equal to -

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

The correct option is A $1$

Given points are $(a,0),(0,b)$ and $(1,1)$

$x_1=a,y_1=0,x_2=0,y_2=b$ and $x-3=1,y_3=1$
Condition for collinearity
$x_1{y}_2+x_2{y}_3+x_3{y}_1=x_2{y}_1+x_3{y}_2+x_1{y}_3$ gives
$ab+0+0=0+1.b+a.1\Rightarrow ab=a+b$
$\Rightarrow 1=\frac{1}{b}+\frac{1}{a}$

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