Pair Of Straight Lines Question 58
Question: If the equation $ 2x^{2}+7xy+3y^{2}-9x-7y+k=0 $ represents a pair of lines, then k is equal to
[Kerala (Engg.) 2002]
Options:
A) 4
B) 2
C) 1
D) - 4
Show Answer
Answer:
Correct Answer: A
Solution:
For this to represent straight lines $ abc+2fgh-af^{2}-bg^{2}-ch^{2}=0 $ Here, a = 2, b = 3, c = k, f = -7/2, g = -9/2, h = 7/2.
Therefore $ 2.3.k+2(-7/2)(-9/2)(7/2)-2{{(-7/2)}^{2}} $
$ -3{{(-9/2)}^{2}}-k{{(7/2)}^{2}}=0 $
Therefore $ 6k+\frac{441}{4}-\frac{49}{2}-\frac{243}{4}-\frac{49k}{4}=0 $
Therefore $ 24k+441-98-243-49k=0 $
Therefore $ -25k+100=0 $
Therefore $ k=4 $ .
BETA
