ple solve this qutn

prove that the locus of center of the circle

1\2(x²+y²)+ x cosA + y sinA - 4 = 0

is x²+ y² = 1

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Dear rohan

1\2(x²+y²)+ x cosA + y sinA - 4 = 0

or (x²+y²)+ 2x cosA + 2y sinA - 8 = 0

center of circle is (-cosA ,-sinA)

let center of circle is (h,k)

 so h=-cosA   and k=-sinA

h²+k² =sin²A +cos²A

h²+k² =1

so locus

x²+^y2 =1