Circle And System Of Circles Question 305
Question: The two circles $ x^{2}+y^{2}-2x+22y+5=0 $ and $ x^{2}+y^{2}+14x+6y+k=0 $ intersect orthogonally provided k is equal to
[Karnataka CET 2005]
Options:
A) 47
B) $ -47 $
C) 49
D) $ -49 $
Show Answer
Answer:
Correct Answer: A
Solution:
Given two circles $ x^{2}+y^{2}-2x+22y+5=0 $
$ x^{2}+y^{2}+14x+6y+k=0 $
The two circles cut orthogonally, if $ 2(g_1g_2+f_1f_2)=c_1+c_2 $ i.e., $ 2(-1.7+11.3)=5+k $
$ 2(-7+33)=5+k\Rightarrow 52-5=k\Rightarrow k=47 $ .
BETA
