Question

The intercept cut-off by a line from y-axis is twice than from x-axis and the line passes through the point (1, 2). The equation of the line is
(a) 2x + y = 4
(b) 2x + y + 4 = 0
(c) 2x – y = 4
(d) 2x – y + 4 = 0

Answer 1

Let us suppose line make intercept "a" an x-axis.
Then according to given condition, it makes intercept 2a an y-axis
i.e. equation of the line is given by
$$\begin{gathered} \frac{x}{a}+\frac{y}{2a}=1 \\ \mathrm{i}.\mathrm{e}.2x+y=2a \end{gathered}$$
also given line passes through (1, 2)
i.e. 2(1) + 2 = 2a
i.e. 4 = 2a
i.e. a = 2
∴ equation of line is 2x + y = 4

Hence, the correct answer is option A.