Question

a line makes positive intercepts on coordinate axis whose sum is 7 and it passes through(-3,8) find the equation​

Answer 1

Step-by-step explanation :

Let us take the equation of a line in intercept form as follows,

x/a + y/b = 1 ..... (i)

By the given condition,

a + b = 7 ..... (ii)

Also given that, (i) no. line passes through the point (- 3, 8). Then from (i), we write

- 3/a + 8/b = 1

or, - 3b + 8a = ab

or, - 3 (7 - a) + 8a = a (7 - a), by (ii)

or, - 21 + 3a + 8a = 7a - a²

or, a² + 4a - 21 = 0

or, a² + 7a - 3a - 21 = 0

or, a (a + 7) - 3 (a + 7) = 0

or, (a + 7) (a - 3) = 0

Either a + 7 = 0 or, a - 3 = 0

i.e., a = - 7, 3

Given that a > 0; then a = 3 only.

Then b = 4.

From (i), we get the equation of the required line

x/3 + y/4 = 1

or, 4x + 3y = 12 .