Pair Of Straight Lines Question 148
Question: The values of h for which the equation $ 3x^{2}+2hxy-3y^{2}-40x+30y-75=0 $ represents a pair of straight lines, are
[MP PET 1989]
Options:
A) 4, 4
B) 4, 6
C) 4, - 4
D) 0, 4
Show Answer
Answer:
Correct Answer: A
Solution:
We have $ abc+2fgh-af^{2}-bg^{2}-ch^{2}=0 $
$ \Rightarrow (3)(-3)(-75)+2(15)(-20)(h) $
$ -3{{(15)}^{2}}-(-3){{(-20)}^{2}}-(-75)h^{2}=0 $
$ \Rightarrow 675-600h-675+1200+75h^{2}=0 $
$ \Rightarrow h=4,4. $
BETA
