Point P which lies on the line y = can be chosen as P . If θ be the angle that the line y = makes with the +ve direction of the X-axis, then

tan θ = ⇒ cos θ = and sin θ =

Now, coordinates of points A and B which lie on the line y = can be chosen as

A ≡ and B ≡

Since A lies on the line x – y + 1 = 0, therefore

– + 1 = 0 gives

r 1 = (h + 4)

and B lies on the line 2x – y – 5 = 0, therefore

2 – – 5 = 0 gives

r 2 = (h – 4)

According to the given condition, we have

PA · PB = 25

i.e. |r 1 | · |r 2 | = 25

i.e. (h 2 – 16) = ± 25

i.e. h 2 = 16 ± 16 = 32, 0 gives h = ±4 , 0

Hence, the required points, are (0, 0), (4 , 3 ) and (–4 , –3 ).