Question

Is the linear equation aX + B Y + c equal to zero and lX + mY + n equal to zero represents the same line and R equal to l/a
equal to N/
C write the value of R in terms of M and b

Answer 1

Answer:

Explanation:

Lines L1 = ax + by + c = 0 and L2 = lx + my + n = 0 intersect at the point P and makes an angle A with each other. Find the equation of a line L ...

Answer 2

The value of R in terms of m and b is , R = $\frac{m}{b}$

• Let us assume $\frac{l}{a} = \frac{n}{c} = k$ where k is non zero.
• hence l = ak and n = ck. now putting the value of this in the second equation we get, akx+my+ck=0

• taking common k we get, k(ax+$\frac{m}{k}$y+c) = 0
• now ax+c= -by. Putting this in the previous equation we get, k[($\frac{m}{k}$-b)y] = 0
• now as k is non zero then $\frac{m}{k} -b$ = 0, which implies k=m/b
• But we know R = $\frac{l}{a} = \frac{n}{c} = k$. So R = m/b
• Hence the required representation of R is m/b.