Question

A line through A (- 5, - 4) meets the line x + 3y + 2 = 0, 2x + y + 4 = 0 and x - y - 5 = 0 at the points B, C and D respectively. If (15/AB)² + (10/AC)², find the equation of the line.

Answer 1

Let equation of line AC is

Let line AE lf make angle θ with x-axis and intersccts x + 3y + 2 = 0 at B at a distance r₁ and line 2x + y + 4 = 0 at C at a distance r₂ and line x - y - 5 = 0 at D at a distance r₃.

But it is given that

 

which is the equation of required straight line.