InterviewSolution
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InterviewSolution
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Circles are drawn on chords of the rectangular hyperbola xy = 4 parallel to the line y = x as diameters. All such circles pass through two fixed points whose coordinates areA. (2, 2)B. (2, -2)C. `(-2, 2)`D. `(-2, -2)` |
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Answer» Correct Answer - A::D The circle with points `P(2t_(1),2//t_(1))` and `Q(2t_(2),2//t_(2))` as diameter is given by `(x-2t_(1))(x-2t_(2))+(y-(2)/(t_(1)))(y-(2)/(t_(2)))=1" (1)"` Also, the slope of PQ is given by `-(1)/(t_(1)t_(2))=1 or t_(1)t_(2)=-1` Hence, from (1), the circle is `(x^(2)+y^(2)-8)-2(t_(1)+t_(2))(x-y)=0` which is of the form `S+lambdaL=0`. Hence, circles pass through the points of intersection of the circle `x^(2)+y^(2)-8=0` and the line x = y. The point of intersection are (2, 2) and `(-2, -2)`. |
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