First slide

Equation of line in Straight lines

Question

If a straight line cuts intercepts from the axes of coordinates the sum of the reciprocals of which is a constant k, then the line passes through the fixed point

Moderate

A

(k, k)
B

$(\frac{1}{k}, \frac{1}{k})$
C

(k, –k)
D

(–k, k)

Solution

Let the equation of the line be
$\frac{x}{a} + \frac{y}{b} = 1$ (1)
Its intercepts on x-axis and y-axis are a and b respectively.
Given: $\frac{1}{a} + \frac{1}{b} = k$
$\Rightarrow \frac{1}{a k} + \frac{1}{b k} = 1 o r \frac{1 / k}{a} + \frac{1 / k}{b} = 1$ (2)
From (2) it follows that the line (1) passes through the fixed point
$(\frac{1}{k}, \frac{1}{k})$

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