Circle And System Of Circles Question 185
Question: If $ (\alpha ,\beta ) $ is the centre of a circle passing through the origin, then its equation is
[MP PET 1999]
Options:
A) $ x^{2}+y^{2}-\alpha x-\beta y=0 $
B) $ x^{2}+y^{2}+2\alpha x+2\beta y=0 $
C) $ x^{2}+y^{2}-2\alpha x-2\beta y=0 $
D) $ x^{2}+y^{2}+\alpha x+\beta y=0 $
Show Answer
Answer:
Correct Answer: C
Solution:
Radius = Distance from origin $ =\sqrt{{{\alpha }^{2}}+{{\beta }^{2}}} $
$ \therefore $ $ {{(x-\alpha )}^{2}}+{{(y-\beta )}^{2}}={{\alpha }^{2}}+{{\beta }^{2}} $
$ \Rightarrow x^{2}+y^{2}-2\alpha x-2\beta y=0 $ .
BETA
