Circle And System Of Circles Question 222
Question: The centre of the circle $ x=2+3\cos \theta $ , $ y=3\sin \theta -1 $ is
[Karnataka CET 2005]
Options:
A) (3, 3)
B) $ (2,-1) $
C) $ (-2,1) $
D) $ (-1,2) $
Show Answer
Answer:
Correct Answer: B
Solution:
$ x=2+3\cos \theta ,y=3\sin \theta -1 $
$ x^{2}+y^{2}=4+9{{\cos }^{2}}\theta +12\cos \theta +9{{\sin }^{2}}\theta +1-6\sin \theta $
$ =14+12\cos \theta -6\sin \theta $ = $ 4(2+3\cos \theta )-2(3\sin \theta -1)+4 $
therefore $ x^{2}+y^{2}=4x-2y+4 $
therefore $ (x^{2}-4x+4)+(y^{2}+2y+1)=9 $
therefore $ {{(x-2)}^{2}}+{{(y+1)}^{2}}=9 $ , \ centre is $ (2,-1) $ .
BETA
