1.

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.

Answer»


SOLUTION :`C_(1)-=(1,1),C_(2)-=(9, 6),r_(1)=1, r_(2)=2`
`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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