Question

Find the equation of the straight line passing through the origin and the point of intersection of the lines x/a + y/b = 1 and x/b + y/a = 1.

Answer 1

Solution :

Since the required line passes through the point of intersection of the lines x/a + y/b = 1 and x/b + y/a = 1, let us consider its equation to be

(x/a + y/b - 1) + k (x/b + y/a - 1) = 0 ...(i)

Given that, (i) no. line passes through the origin. Then

- 1 + k (- 1) = 0

or, - 1 - k = 0

or, k = - 1

Putting k = - 1 in (i), we get the required straight line as

x/a + y/b - 1 - x/b - y/a + 1 = 0

or, (1/a - 1/b)x - (1/a - 1/b)y = 0

or, x - y = 0

or, x = y

Answer 2

Answer:

Find the equation of the straight line passing through the origin and the point of intersection of the lines x/a+y/b=1 and x/b+y/a=1