Circle And System Of Circles Question 63
Question: A line through (0,0) cuts the circle $ x^{2}+y^{2}-2ax=0 $ at A and B, then locus of the centre of the circle drawn on AB as a diameter is
[RPET 2002]
Options:
A) $ x^{2}+y^{2}-2ay=0 $
B) $ x^{2}+y^{2}+ay=0 $
C) $ x^{2}+y^{2}+ax=0 $
D) $ x^{2}+y^{2}-ax=0 $
Show Answer
Answer:
Correct Answer: D
Solution:
Let chord AB is $ y=mx $ …..(i) Equation of CM, $ x+my=\lambda $ It is passing through (a, 0)
$ \therefore $ $ x+my=a $ …..(ii)
From (i) and (ii), $ x+y.,\frac{y}{x}=a $
therefore $ x^{2}+y^{2}=ax $
$ \Rightarrow $ $ x^{2}+y^{2}-ax=0 $ is the locus of the centre of the circle.
BETA
