InterviewSolution
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InterviewSolution
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The real numbers a and b are distinct. Consider the circles `omega_(1): (x-a)^(2)+ (y-b)^(2) = a^(2)+b^(2)` and `omega_(2): (x-b)^(2) +(y-a)^(2) = a^(2) +b^(2)` Which of the following is (are) true?A. The line `y = x` is an axis of symmetry for the circlesB. The circles intersect at the origin and a point, P(say), which lies on the line `y = x`C. The line `y = x` is the radical axis of the pair of circles.D. The circles are orthogonal for all `a ne b`. |
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Answer» Correct Answer - A::B::C Interchanging x and y in one equation gives the other equation. So, (a) is true, Clearly (0,0) satisfies both circles and `y = x` is radical axis. So (b) and (c ) are true. The centres are (a,b) and (b,a) the radii are both `sqrt(a^(2)+b^(2))`. The distance between the centres `= |a-b| sqrt(2)` If circles are orthogonal, `|a-b| sqrt(2) = 2(a^(2)+b^(2))` Now, `2(a^(2)+b^(2)) ne 2(a^(2)-b^(2))`, for all a and b. Thus, (d) is false. |
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