Circle And System Of Circles Question 97
The equation of the circle which touches both axes and whose centre is $ (a,\ b) $ is
[MP PET 1988]
Options:
A) $ x^{2}+y^{2}+2x_1(x+y)+x_1^{2}=0 $
B) $ x^{2}+y^{2}-2x_1(x+y)+x_1^{2}=0 $
C) $ x^{2}+y^{2}=x_1^{2}+y_1^{2} $
D) $ x^{2}+y^{2}+2x x_1+2y y_1=0 $
Show Answer
Answer:
Correct Answer: B
Solution:
The equation will be $ {{(x-x_1)}^{2}}+{{(y-y_1)}^{2}}=r^{2} $ As the circle touches both the axes, $ (r)=\sqrt{{{(r)}^{2}}+{{(r)}^{2}}}=r\sqrt{2} $ \ $ {{(x-r)}^{2}}+{{(y-r)}^{2}}=r^{2} $
therefore $ x^{2}+y^{2}-2x_1(x+y)+x_1^{2}=0 $ .
BETA
