Prove that the locus of the centre of the circle is .

MATHEMATICS · Subjective · CBSE · Mathematics · Conic Sections · Conic Sections

Problem

Prove that the locus of the centre of the circle 12(x2+y2)+xcos⁡θ+ysin⁡θ−4=0\frac{1}{2}(x^2 + y^2) + x \cos \theta + y \sin \theta - 4 = 0 is x2+y2=1x^2 + y^2 = 1 .

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