Pair Of Straight Lines Question 83
Question: The equation $ 4x^{2}+12xy+9y^{2}+2gx+2fy+c=0 $ will represents two real parallel straight lines, if
Options:
A) g = 4, f = 9, c = 0
B) g = 2, f = 3, c = 1
C) g = 2, f = 3, c is any number
D) g = 4, f = 9, c > 1
Show Answer
Answer:
Correct Answer: C
Solution:
The lines are parallel, if $ h^{2}=ab,af^{2}=bg^{2} $
or $ \frac{a}{h}=\frac{h}{b}=\frac{g}{f}\Rightarrow 4f^{2}=9g^{2} $
$ \Rightarrow f=\frac{3}{2}g\Rightarrow g=2,\ \ f=3 $ (let)
Now $ abc+2fgh-af^{2}-bg^{2}-ch^{2}=0 $
$ \Rightarrow 4\times 9\times c+2\times 3\times 2\times 6-4{{(3)}^{2}}-9{{(2)}^{2}}-c{{(6)}^{2}}=0 $
$ \Rightarrow $ c is any number.
BETA
