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ple solve this qutn prove that the locus of center of the circle 1\2(x 2 +y 2 )+ x cosA + y sinA - 4 = 0 is x 2 + y 2 = 1

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





Grade:11

1 Answers

Badiuddin askIITians.ismu Expert
148 Points
13 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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