Question

The straight line whose sum of the intercepts on the axes is equal to half of the product of the intercepts passes through the point

• A. $\left(1,1\right)$
• B. $\left(2,2\right)$
• C. $\left(3,3\right)$
• D. $\left(4,4\right)$

Answer 1

The correct option is B

$\left(2,2\right)$

Explanation for the correct option:

Equation of a line in intercept form is

$$\begin{gathered} \frac{x}{a}+\frac{y}{b}=1 \\ \Rightarrow bx+ay=ab...\left(1\right) \end{gathered}$$

Where $a$ is the $x$-intercept and $b$ is the $y$-intercept.

Given, sum of the intercepts on the axes is equal to half of the product of the intercepts.

So,

$$\begin{gathered} a+b=\frac{ab}{2} \\ \Rightarrow ab=2a+2b...\left(2\right) \end{gathered}$$

Comparing $\left(1\right)$ with $\left(2\right)$

$bx+ya=2a+2b$

Comparing both sides

$y=2,x=2$

Thus, the line passes through $(2,2)$.

Hence, option B is correct.