Question

If $u=a_{1}x+b_{1}y+c_1=0,v=a_{2}x+b_{2}y+c_2=0$ and $\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$, then the curve $u+kv=0$ is

• A. the same straight line $u$
• B. different straight line
• C. not a straight line
• D. None of these

Answer 1

The correct option is A the same straight line $u$

Given $\frac{a_1}{a_2}=\frac{b_{!}}{b_2}=\frac{c_1}{c_2}$

Let above ratios be equal to some constant $\frac{1}{m},$

then $a_2=m{a}_1,b_2=m{b}_1,c_2=m{c}_1$

now equation $v=0$ turns into $mu=0$ $\to$ equations $v$ and $u$ are basically one and the same .

Hence their summation will lead to some multiple of $u$ again.