Question

Find the equation of the line which cuts off equal and positive intercepts from the axes and passes through the point (alpha, bita).

Answer 1

Let the equation be of the form x+y=a, now this equation satisfies (alpha,bita), thus substituting the point in the line considered we get, a=(alpha+bita). Therefore, the equation of the line is x+y=(alpha+bita).

Answer 2

Given:

The points through which the line passes=(alpha, beta)

To find:

Equation of the line which cuts off equal and positive intercepts from the axes and passes through the given point

Solution:

We can find the equation by following the given process-

We know that the equation of the line can be formed by using the given point.

The line is cutting off equal and positive intercepts.

Let these intercepts be (a, a).

The equation of the line= x/a+y/b=1

where x and y are the points through which the line passes.

So,

$(x, y)=( \alpha, \: \beta )$

The equation thus formed is as follows-

$\frac{ \alpha }{ a } + \frac{ \beta }{a} = 1$

$\frac{ \alpha + \beta }{a} = 1$

$\alpha + \beta = a$

$\alpha + \beta - a = 0$

Therefore, the equation of the line which cuts off equal and positive intercepts from the axes and passes through the (alpha, beta) is alpha+beta-a=0.