Pair Of Straight Lines Question 122
Question: The pair of lines represented by $ 3ax^{2}+5xy+(a^{2}-2)y^{2}=0 $ are perpendicular to each other for
[AIEEE 2002]
Options:
A) Two values of $ a $
B) $ \forall a $
C) For one value of $ a $
D) For no value of $ a $
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Answer:
Correct Answer: A
Solution:
$ \because $ The lines are perpendicular, if coefficient of $ x^{2} $ + coefficient of $ y^{2}=0 $
Therefore $ 3a+(a^{2}-2)=0 $
Therefore $ a^{2}+3a-2=0 $
$ \because $ The equation is a quadratic equation in a and $ B^{2}-4AC>0 $ .
The roots of a are real and distinct. Therefore, the lines are perpendicular to each other for two values of a.
BETA
