Circle And System Of Circles Question 78
Question: The locus of the middle points of those chords of the circle $ x^{2}+y^{2}=4 $ which subtend a right angle at the origin is
[MP PET 1990; IIT 1984; RPET 1997; DCE 2000, 01]
Options:
A) $ x^{2}+y^{2}-2x-2y=0 $
B) $ x^{2}+y^{2}=4 $
C) $ x^{2}+y^{2}=2 $
D) $ {{(x-1)}^{2}}+{{(y-2)}^{2}}=5 $
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Answer:
Correct Answer: C
Solution:
Let the mid-point of chord is (h,k). Also radius of circle is 2. Therefore $ \frac{OC}{OB}=\cos 45^{o}\Rightarrow \frac{\sqrt{h^{2}++k^{2}}}{2}=\frac{1}{\sqrt{2}}\Rightarrow h^{2}+k^{2}=2 $
Hence locus is $ x^{2}+y^{2}=2 $ .
BETA
