Circle And System Of Circles Question 294
Question: A circle passes through (0, 0) and (1, 0) and touches the circle $ x^{2}+y^{2}=9 $ , then the centre of circle is
[IIT 1992]
Options:
A) $ ( \frac{3}{2},\frac{1}{2} ) $
B) $ ( \frac{1}{2},\frac{3}{2} ) $
C) $ ( \frac{1}{2},\frac{1}{2} ) $
D) $ ( \frac{1}{2},\ \pm \sqrt{2} ) $
Show Answer
Answer:
Correct Answer: D
Solution:
Radius of the circle $ r=\frac{3}{2} $
$ \frac{1}{4}+k^{2}=\frac{9}{4}\Rightarrow k=\pm \sqrt{2} $
Hence centre is $ ( \frac{1}{2},\ \pm \frac{\sqrt{2}}{2} ) $.
BETA
