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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Grade 11Analytical Geometry

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

rohan bhatia

16 Years agoGrade 11

1 Answer

Badiuddin askIITians.ismu Expert

16 Years ago

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

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