Prove that the following sets of three lines are concurrent: (i) 15 x�

1.	Prove that the following sets of three lines are concurrent: (i) 15 x−18 y+1=0, 12 x+10 y−3=0 and 6 x+66 y−11=0 (ii) 3 x−5 y−11=0, 5 x+3 y−7=0 and x+2 y=0 (iii) xa+yb=1, xb+ya=1 and y=x.
Answer» Prove that the following sets of three lines are concurrent: $(i) 15 x - 18 y + 1 = 0, 12 x + 10 y - 3 = 0$ and $6 x + 66 y - 11 = 0$ $(i i) 3 x - 5 y - 11 = 0, 5 x + 3 y - 7 = 0$ and $x + 2 y = 0$ $(i i i) \frac{x}{a} + \frac{y}{b} = 1, \frac{x}{b} + \frac{y}{a} = 1$ and $y = x .$

Prove that the following sets of three lines are concurrent: (i) 15 x−18 y+1=0, 12 x+10 y−3=0 and 6 x+66 y−11=0 (ii) 3 x−5 y−11=0, 5 x+3 y−7=0 and x+2 y=0 (iii) xa+yb=1, xb+ya=1 and y=x.

Answer»

Prove that the following sets of three lines are concurrent:

$(i) 15 x - 18 y + 1 = 0, 12 x + 10 y - 3 = 0$ and $6 x + 66 y - 11 = 0$

$(i i) 3 x - 5 y - 11 = 0, 5 x + 3 y - 7 = 0$ and $x + 2 y = 0$

$(i i i) \frac{x}{a} + \frac{y}{b} = 1, \frac{x}{b} + \frac{y}{a} = 1$ and $y = x .$