Circle And System Of Circles Question 102
Question: The equation of the circle which passes through the origin, has its centre on the line $ x+y=4 $ and cuts the circle $ x^{2}+y^{2}-4x+2y+4=0 $ orthogonally, is
Options:
A) $ x^{2}+y^{2}-2x-6y=0 $
B) $ x^{2}+y^{2}-6x-3y=0 $
C) $ x^{2}+y^{2}-4x-4y=0 $
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
Equation of circle with centre $ (-g,\ -h) $ and passing through origin is $ x^{2}+y^{2}+2gx+2fy=0 $ …………. (i) and $ g+h+4=0 $ …………. (ii) Also $ -4g+2f=4 $ …………. (iii) (ii) and (iii) give g and f, which will give the desired equation $ x^{2}+y^{2}-4x-4y=0 $ .
BETA
