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Find number of integral values of k for which the line3x + 4y - k = 0 , lies between the circlesx^2 + y^2 - 2x - 2y + 1 = 0 andx^2 + y^2 - 18 x - 12 y + 113 = 0, without cutting a chord on either of circle. |
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Answer» `C_(1)M_(1)ger_(1)` `C_(2)M_(2)ger_(2)` `|(3+4-k)/(5)|GE1` `|7-k|ge5""C_(1)" is below the LINE "3x+4y-k=0` `k-7ge5""7-klt0` `kge12"....(i)"` `|27+25-k|ge10""C_(2)" lies above the line "3x+4y-k=0` `51-k gr10""51-k gt0` `kle41"....(ii)"` From (i) and (ii) `k in [12, 41]"Number of INTEGRAL value = 30"` |
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