Circle And System Of Circles Question 53
Question: The equation of the circle which intersects circles $ x^{2}+y^{2}+x+2y+3=0 $ , $ x^{2}+y^{2}+2x+4y+5=0 $ and $ x^{2}+y^{2}-7x-8y-9=0 $ at right angle, will be
Options:
A) $ x^{2}+y^{2}-4x-4y-3=0 $
B) $ 3(x^{2}+y^{2})+4x-4y-3=0 $
C) $ x^{2}+y^{2}+4x+4y-3=0 $
D) $ 3(x^{2}+y^{2})+4(x+y)-3=0 $
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Answer:
Correct Answer: D
Solution:
Let circle be $ x^{2}+y^{2}+2gx+2fy+c=0 $ . Then according to the conditions given, $ g+2f=c+3 $ …………. (i)
$ 2g+4f=c+5 $ …………. (ii)
$ -7g-8f=c-9 $ …………. (iii)
$ \Rightarrow g=\frac{2}{3},\ f=\frac{2}{3},\ c=-1 $
Therefore, the required equation is $ 3(x^{2}+y^{2})+4(x+y)-3=0 $ .
BETA
