Straight Line Question 388
Question: The equations $ (b-c)x+(c-a)y+(a-b)=0 $ and $ (b^{3}-c^{3})x+(c^{3}-a^{3})y+a^{3}-b^{3}=0 $ will represent the same line, if
Options:
A)b = c
B)c = a
C)a = b
D)a + b + c = 0
Show Answer
Answer:
Correct Answer: E
Solution:
- (e) The two lines will be identical if there exists some real number k such that $ b^{3}-c^{3}=k(b-c), $ $ c^{3}-a^{3}=k(c-a) $ , $ a^{3}-b^{3}=k(a-b) $
Þ $ b-c=0 $ or $ b^{2}+c^{2}+bc=k $
Þ $ c-a=0 $ or $ c^{2}+a^{2}+ac=k $
Þ $ a-b=0 $ or $ a^{2}+b^{2}+ab=k $
Þ $ b=c,c=a,a=b $ or $ b^{2}+c^{2}+bc=c^{2}+a^{2}+ca $
Þ $ b^{2}-a^{2}=c(a-b)\Rightarrow b=a $ or $ a+b+c=0 $ .
BETA
