Question

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

• A. $0$
• B. $\frac{1}{2}$
• C. $2$
• D. $1$

Answer 1

The correct option is D $1$

Let $A(a,0),B(0,b)$ and $C(1,1)$ be the coordinates of a straight line

$\Rightarrow$ Slope of $AB=$Slope of $BC$

Slope of a line is$\frac{y_2-y_1}{x_2-x_1}$

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

$\Rightarrow b=-a(1-b)$

$\Rightarrow b=-a+ab$

$\Rightarrow a+b=ab$

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

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