Question

A straight line passes through the point (alpha,beta) and this point bisects the part of the line intercepted between the axes.show that the equation of the straight line is x/alpha+y/beta=1

Answer 1

RHS of the answer given above is not correct... should be 2.

Let the x and y intercepts of the straight line be a (point A) and b (point B) respectively.

equation of the line:   x/a + y/b = 1

Since the point (α, β) bisects AB,   α = a/2   and  β = b/2
      so equation of straight line =  x/α + y/β = 2