Circle And System Of Circles Question 229
Question: If one end of the diameter is (1, 1) and other end lies on the line $ x+y=3 $ , then locus of centre of circle is
[AMU 2005]
Options:
A) $ x+y=1 $
B) $ 2(x-y)=5 $
C) $ 2x+2y=5 $
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
The other end is $ (t,,3-t) $ So the equation of the variable circle is $ (x-1)(x-t)+(y-1)(y-3+t)=0 $ or $ x^{2}+y^{2}-(1+t)x-(4-t)y+3=0 $
The centre $ (\alpha ,\beta ) $ is given by $ \alpha =\frac{1+t}{2},\beta =\frac{4-t}{2} $
therefore $ 2\alpha +2\beta =5 $
Hence, the locus is $ 2x+2y=5 $ .
BETA
