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If one end of the diameter is (1, 1) and...

If one end of the diameter is (1, 1) and the other end lies on the line `x+y=3` , then find the locus of the center of the circle.

Text Solution

Verified by Experts

The correct Answer is:
`2x+2y-5=0`
Let C(h,k) be the centre and AB be the diameter of the circle.

`:. B-=(2h-1,2k-1)`
Point B lies on the line `x+y-3=0`
`:. 2h-1+2k-1-3=0`
Hence, required locus is `2x+2y-5=0`.
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