A variable point P lies on the line L = 0 . Tangents from P touch the circle x 2 + y 2 = 4 at Q , R , and parallelogram PQSR is completed. If L is 2 x + y = 6 , then the locus of the circumcentre of △

Question

A variable point P lies on the line L = 0 . Tangents from P touch the circle x 2 + y 2 = 4 at Q , R , and parallelogram PQSR is completed. If L is 2 x + y = 6 , then the locus of the circumcentre of △ PQR is

TestHub · Accepted Answer

Since ∠ PQO = ∠ PRO = 9 0 ∘ for O = ( 0 , 0 ) , the circumcircle of PQR has diameter PO , so its centre is P /2 . Halving the equation of P gives 2 x + y = 3 .

Mathematics - Circle Question with Solution | TestHub

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