Circle And System Of Circles Question 204
Question: A variable circle passes through the fixed point (2,0) and touches the y-axis . Then the locus of its centre is
[EAMCET 2002]
Options:
A) A circle
B) An Ellipse
C) A hyperbola
D) A parabola
Show Answer
Answer:
Correct Answer: D
Solution:
Suppose the centre of circle be $ (h,k) $ . Since it touches the $ y\text{-axis} $ ,
$ \therefore $ radius of circle = h Now $ {{(h-2)}^{2}}+k^{2}=h^{2} $
$ \Rightarrow $ $ h^{2}+4-4h+k^{2}=h^{2} $
$ \Rightarrow $ $ k^{2}=4h-4 $ .
Hence the locus of centre is $ y^{2}=4x-4 $ , which is a parabola.
BETA
