Circle And System Of Circles Question 223
Question: A circle touches the x-axis and also touches the circle with centre at (0, 3) and radius 2. The locus of the centre of the circle is
[AIEEE 2005]
Options:
A) A hyperbola
B) A parabola
C) An ellipse
D) A circle
Show Answer
Answer:
Correct Answer: B
Solution:
Let centre $ \equiv (h,k); $ As $ C_1C_2=r_1+r_2 $ , (Given)
$ \Rightarrow ,\sqrt{{{(h-0)}^{2}}+{{(k-3)}^{2}}}=|k+2| $
therefore $ h^{2}=5(2k-1) $
Hence locus, $ x^{2}=5(2y-1) $ , which is parabola.
BETA
