Circle And System Of Circles Question 280
Question: The centre of the circle, which cuts orthogonally each of the three circles $ x^{2}+y^{2}+2x+17y+4=0, $ $ x^{2}+y^{2}+7x+6y+11=0, $ $ x^{2}+y^{2}-x+22y+3=0 $ is
[MP PET 2003]
Options:
A) (3, 2)
B) (1, 2)
C) (2, 3)
D) (0, 2)
Show Answer
Answer:
Correct Answer: A
Solution:
Let circle $ x^{2}+y^{2}+2gx+2fy+c=0 $ …..(i) Circle (i) cuts orthogonally each of the given three circles. Then according to the condition $ 2g_1g_2+2f_1f_2=c_1+c_2 $ , $ 2g+17f=c+4 $ …..(ii) $ 7g+6f=c+11 $ …..(iii) $ -g+22f=c+3 $ …..(iv)
From (ii), (iii) and (iv), $ g=-3,, $
$ f=-2 $
Therefore, the centre of the circle $ (-g,,-f)=,(3,,2) $ .
BETA
