The equations of the line the reciprocal of whose intercepts on the axes are a and b is given by

Options

A. `x//a+y//b=1`
B. `ax+by=1`
C. `ax+by=ab`
D. `ax-by=1`

Answer

To find the equation of the line whose intercepts on the axes are the reciprocals of \( a \) and \( b \), we can follow these steps:

### Step 1: Identify the intercepts
Given that the reciprocals of the intercepts on the axes are \( a \) and \( b \), the intercepts can be expressed as:
- The x-intercept is \( \frac{1}{a} \)
- The y-intercept is \( \frac{1}{b} \)

### Step 2: Write the intercept form of the line
The equation of a line in intercept form is given by:
\[ \frac{x}{\text{x-intercept}} + \frac{y}{\text{y-intercept}} = 1 \]
Substituting the intercepts we found:
\[ \frac{x}{\frac{1}{a}} + \frac{y}{\frac{1}{b}} = 1 \]

### Step 3: Simplify the equation
We can rewrite the equation as:
\[ ax + by = 1 \]

### Final Equation
Thus, the equation of the line whose intercepts on the axes are the reciprocals of \( a \) and \( b \) is:
\[ ax + by = 1 \]