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a rod PQ of length 2a slides with its ends on the axes. the locus of the circumcentre of triangle OPQ

a rod PQ of length 2a slides with its ends on the axes. the locus of the circumcentre of triangle OPQ

Grade:12

1 Answers

Khimraj
3007 Points
7 years ago
Let at a instant the coordinates of ends of rod are (x,0) and (0,y). Then it will make right angle triangle with origin. And circumcentre of right angled triangle is mod point of hypotenuse. And coordinate of mid point of hypotenuse is (X,Y)=(x/2,y/2). Then apply pythogorous theorem.x² + y² = 4a² . And (x/2)² +(y/2)² = a². Then X² + Y² = a².Hope it clears. If still u have doubts then please clarify. If u like answer then please approve the answer.

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