Circle And System Of Circles Question 73
Question: The locus of the centre of a circle which touches externally the circle $ x^{2}+y^{2}-6x-6y+14=0 $ and also touches the y-axis, is given by the equation
[IIT 1993; DCE 2000]
Options:
A) $ x^{2}-6x-10y+14=0 $
B) $ x^{2}-10x-6y+14=0 $
C) $ y^{2}-6x-10y+14=0 $
D) $ y^{2}-10x-6y+14=0 $
Show Answer
Answer:
Correct Answer: D
Solution:
Let the centre be (h, k), then radius = h Also $ CC_1=R_1+R_2 $ or $ \sqrt{{{(h-3)}^{2}}+{{(k-3)}^{2}}}=h+\sqrt{9+9-14} $
$ \Rightarrow {{(h-3)}^{2}}+{{(k-3)}^{2}}=h^{2}+4+4h $
$ \Rightarrow k^{2}-10h-6k+14=0 $ or $ y^{2}-10x-6y+14=0 $ .
BETA
