Pair Of Straight Lines Question 13
Question: If $ ax^{2}-y^{2}+4x-y=0 $ represents a pair of lines then $ a= $
[Karnataka CET 2004]
Options:
A) - 16
B) 16
C) 4
D) - 4
Show Answer
Answer:
Correct Answer: B
Solution:
Given equation is $ ax^{2}-y^{2}+4x-y=0 $
Here $ A=a,B=-1,H=0,G=2,F=\frac{-1}{2},C=0 $
If the given equation represents a pair of straight lines, then
$ ABC+2FGH-AF^{2}-BG^{2}-CH^{2}=0 $$ 0-0-a( \frac{1}{4} )-(-1)(4)=0 $
Therefore $ \frac{-a}{4}=4=0\Rightarrow a=16 $ .
BETA
