Straight Line Question 382
Question: If $ u=a_1x+b_1y+c_1=0, $ $ v=a_2x+b_2y+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 [MNR 1987]
Options:
A)The same straight line u
B)Different straight line
C)It is not a straight line
D)None of these
Correct Answer: A
Show Answer
Answer:
Solution:
Þ $ a_2=\frac{a_1}{c},b_2=\frac{b_1}{c},c_2=\frac{c_1}{c} $ Given that $ u+kv=0 $
Þ $ a_1x+b_1y+c_1+k(a_2x+b_2y+c_2)=0 $
Þ $ a_1x+b_1y+c_1+k\frac{a_1}{c}x+k\frac{b_1}{c}y+k\frac{c_1}{c}=0 $
Þ $ a_1x( 1+\frac{k}{c} )+b_1y( 1+\frac{k}{c} )+c_1( 1+\frac{k}{c} )=0 $
Þ $ a_1x+b_1y+c_1=0=u $ .
BETA
