x + 2 y + a = 0 intersects x 2 + y 2 = 4 at distinct points A , B . The line 12 x − 6 y − 41 = 0 intersects x 2 + y 2 − 4 x − 2 y + 1 = 0 at distinct points C , D . For which a are A , B , C , D concy

Question

x + 2 y + a = 0 intersects x 2 + y 2 = 4 at distinct points A , B . The line 12 x − 6 y − 41 = 0 intersects x 2 + y 2 − 4 x − 2 y + 1 = 0 at distinct points C , D . For which a are A , B , C , D concyclic?

TestHub · Accepted Answer

A circle through A , B is x 2 + y 2 − 4 + λ ( x + 2 y + a ) = 0 . Equate its coefficients with x 2 + y 2 − 4 x − 2 y + 1 + μ ( 12 x − 6 y − 41 ) = 0 . Solving gives λ = − 8/5 , μ = 1/5 , a = 2 .

Mathematics - Circle Question with Solution | TestHub

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