Pair Of Straight Lines Question 146
Question: If the equation $ hxy+gx+fy+c=0 $ represents a pair of straight lines, then
Options:
A) $ fh=cg $
B) $ fg=ch $
C) $ h^{2}=gf $
D) $ fgh=c $
Show Answer
Answer:
Correct Answer: B
Solution:
$ hxy+gx+fy+c=0, $ Apply $ \Delta ‘=0 $
i.e., $ a’b’c’+2f’g’h’-a’f{{’}^{2}}-b’g{{’}^{2}}-{c}‘h{{’}^{2}}=0 $
Here $ h’=\frac{h}{2},\ g’=\frac{g}{2},\ f’=\frac{f}{2},\ c’=c,\ a’=0,\ b’=0 $
Hence, $ \frac{hgf}{4}-\frac{ch^{2}}{4}=0 $ or $ fg=ch $ .
BETA
