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InterviewSolution
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Three points A,B and C taken on rectangular hyperbola xy = 4 where B(-2,-2) and C(6,2//3). The normal at A is parallel to BC, then |
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Answer» circumcentre of `DeltaABC` is `(2,-2//3)` Let `A(2t,2//t)` Differentiating curve `xy' +y =0` or `y' =- y//x =- 1//t^(2)` Slope of normal at A is `t^(2)` Normal is PARALLEL to BC, which has slope `((2)/(3)+2)/(6+2)=(1)/(3)=t^(2)` `:.t= (1)/(sqrt(3))` `:. A ((2)/(sqrt(3)),2sqrt(3))` ALSO (slope of AB) `xx` (Slope of `AC) =-1` `:. DeltaABC` is a right angled `Delta`. Circum-center of `DeltaABC` is mid-point `BC,(2,-2//3)` Circum-circle of `DeltaABC` is circle on BC as diameter. Orthocenter of `DeltaABC` is at A. |
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