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Number of integral values of `lambda` for which `x^2 + y^2 + 7x + (1-lambda)y + 5 = 0` represents the equation of a circle whose radius cannot exceed 5 is |
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Answer» Correct Answer - 10 values Radius `le5`. `sqrt(((lambda)/(2))^(2)+((1-lambda)/(2))^(2)-5)le5` `implies 2lambda^(2)-2lambda-119le0` `implies (1-sqrt(239))/(2)lelambdale(1+sqrt(239))/(2)` `implies -7.2 lelambdale8.2 ` ( approximately) `implies lambda=-7,-6,-5.....7,8` (1) Also, we must have `((lambda)/(2))^(2)+((1-lambda)/(2))^(2)-5ge0` `implies 2lambda^(2)-2lambda-19ge0` `implies lambdale(1-sqrt(39))/(2)` or `lambdale(1+sqrt(39))/(2)` (2) From (1) and (2) , `lambda = -7,-6,-5,-4,-3,4,5,6,7,8` |
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