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A circle touches the line `y = x` at the point `(2, 2)` and has it centre on y-axis, then square of its radius is |
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Answer» Correct Answer - 8 A circle touches ………… Equation of a circle touching the line `y = x at (2, 2)` is `(x-2)^(2)+(y-2)^(2)+lambda(x-y) = 0` `i.e. x^(2)y^(2)-(4-lambda)x- (4+lambda)y +8 =0` its centre `((4-lambda)/(2), (4+lambda)/(2))` lies on y-axis `:. (4-lambda)/(2) = 0` i.e. `lambda = 4` `:.` the circle is `x^(2)+y^(2)8y+8=0` `:.` radius `= sqrt(16-8) = sqrt(8)` |
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