Circle And System Of Circles Question 21
Question: If a circle passes through the points of intersection of the coordinate axis with the lines $ \lambda x-y+1=0 $ and $ x-2y+3=0 $ , then the value of $ \lambda $ is
[IIT 1991]
Options:
A) 1
B) 2
C) 3
D) 4
Show Answer
Answer:
Correct Answer: B
Solution:
Points of intersection with co-ordinate axes are $ ( -\frac{1}{\lambda },\ 0 )\text{ },\ (0,\ 1) $ and $ (-3,\ 0),\ ( 0,\ \frac{3}{2} ) $ . Equation of circle through (0, 1), (-3, 0) and $ ( 0,\ \frac{3}{2} ) $ is $ x^{2}+y^{2}+\frac{7x}{2}-\frac{5y}{2}+\frac{3}{2}=0 $ . It passes through $ ( \frac{-1}{\lambda },\ 0 ) $
$ \Rightarrow \frac{1}{{{\lambda }^{2}}}-\frac{7}{2\lambda }+\frac{3}{2}=0\Rightarrow 3{{\lambda }^{2}}-7\lambda +2=0 $
$ \Rightarrow \lambda =\frac{7\pm \sqrt{49-24}}{6}=\frac{7\pm 5}{6}=2,\ \frac{1}{3} $ .
BETA
