Question

A line cuts equal intercepts with positive direction of both the axes and passes through the point (6, 6). The equation of the line is ______.

पर्याय

• x − y = 12

• x − y = 0

• x + y = 6

• x + y = 12

Answer 1

A line cuts equal intercepts with positive direction of both the axes and passes through the point (6, 6). The equation of the line is x + y = 12.

Explanation:

By intercept form :

Equation of line: `x/a + y/b = 1` .........(1)

Given,

Line cuts equal intercepts with both the axes.

∴ x-intercept (a) = y-intercept (b) = p (let)

Given,

Line passes through point (6, 6). So it will satisfy the equation (1).

Substituting values in equation we get:

⇒ `6/p​ + 6/p ​= 1`

⇒ `12/p​ = 1`

⇒ p = 12

∴ a = b = 12

Substituting value of a and b in equation (1), we get:

⇒ `x/12 ​+ y/12 ​= 1`

⇒ `(x + y)/12 ​= 1`

⇒ x + y = 12