Question

A straight line moves so that the sum of the reciprocals of its intercepts on two perpendicular lines is constant, then the line passes through

• A. A fixed point
• B. A variable point
• C. Origin
• D. None

Answer 1

Answer: (A)

A fixed point

$\text{Equation of line in intercept form is}\frac{x}{a}+\frac{y}{b}=1$

$\text{Given that,}\frac{1}{a}+\frac{1}{b}=\text{constant}=\frac{1}{k}\left(\text{say}\right)$

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

$\text{So,}(k,k)\text{lies on}\frac{x}{a}+\frac{k}{b}=1$

$\text{Hence, the line passes through the fixed point}(k,k).$