UPSC NDA Math Model Paper 8

L1;(P−1)x+y−5=0
⇒y=−(P−1)x+5
⇒y=(1−P)x+5
We know y = mx + c, where m = slope, comparing the above equation, we get:
∴ Slope = (1 - P) ----(1)
L2;(2−P)x−3y+2=0
⇒ 3y = (2 - P)x + 2
⇒ y = (2 - P)x / 3 + 2 / 3
We know y = mx + c, where m = slope, comparing the above equation, we get:
∴ Slope = (2 - P) / 3 ----(2)
Now, (1 - P) = (2 - P) / 3
⇒ (3 - 3P) = (2 - P)
⇒ (3P - P) = (3 - 2)
⇒ 2P = 1
⇒ P = 1 / 2