Question

If (a, −2a), a > 0 is the mid-point of a line segment intercepted between the co-ordinate axes, then the equation of the line is ____________.

Options

• x − 2y + 4a = 0

• 2x − y = 4a

• x − 2y = 5a

• 2x − y + 4a = 0

Answer 1

If (a, −2a), a > 0 is the mid-point of a line segment intercepted between the co-ordinate axes, then the equation of the line is 2x − y = 4a.

Explanation:

Let (A, 0) and (0, B) are x and y intercept respectively,

∴ Equation of line is

`"x"/"A" + "y"/"B"` = 1

Now, (a, −2a) is mid-point of intercept

∴ a = `"A"/2` and −2a = `"B"/2`

A = 2a and B = −4a

∴ Required equation of line is

`"x"/(2"a") - "y"/(4"a")` = 1

2x − y = 4a