Circle And System Of Circles Question 304
Question: If the circles $ x^{2}+y^{2}+2ax+cy+a=0 $ and $ x^{2}+y^{2}-3ax+dy-1=0 $ intersect in two distinct points $ P $ and $ Q $ then the line $ 5x+by-a=0 $ passes through $ P $ and $ Q $ for
[AIEEE 2005]
Options:
A) Infinitely many values of $ a $
B) Exactly two values of $ a $
C) Exactly one value of $ a $
D) No value of $ a $
Show Answer
Answer:
Correct Answer: D
Solution:
Equation of line PQ (i.e., common chord) is $ 5ax+(c-d)y+a+1=0 $ …..(i)
Also given equation of line PQ is $ 5x+by-a=0 $ ….. (ii)
Therefore $ \frac{5a}{5}=\frac{c-d}{b}=\frac{a+1}{-a}; $ As $ \frac{a+1}{-a}=a $
therefore $ a^{2}+a+1=0 $ Therefore no real value of a exists, (as D<0).
BETA
