Que. Find the equation of the straight line that passes through the point A(-5,-4)and is such that the portion intercepted between the axes is divided by the point A in the ratio 1:2??

Let the required straight line be (x/a) + (y/b) = 1.  

Using the given conditions, P (2a+1.0/2+1, 2.0+1.b/2+1) is the point which divides (a, 0) and (0, b) internally in the ratio 1 : 2.

Hence –5 = 2a/3, 4 = b/3 ⇒ a = –15/2, b = 12.

⇒ tan θ = –√8 = slope of line.

We know that the equation of the straight line passing through the point (x1, y1) having slope m is y – y1 = m(x – x1).

Therefore the equation of the required line is y – 2 = –√8 (x – 1)

⇒ √8 x + y – √8 – 2 = 0.

Regards

Arun (askIITians forum expert)