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If the circle `x^2+y^2=1`is completely contained in the circle `x^2+y^2+4x+3y+k=0`, then find the values of `kdot` |
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Answer» Given circles are `x^(2)+y^(2)=1` (1) and `x^(2)+y^(2)+4x+3y+k=0` (2) `C_(1)(0,0),r_(1)=1` `C_(2)(-2,-3//2),r_(2)=sqrt(4+(9)/(4)-k)=sqrt((25)/(4)-k)`. Circle (1) is completely contained by circle (2). `implies C_(1)C_(2) lt r_(2) -r_(1)` `implies sqrt(4+(9)/(4))ltsqrt((25)/(4)-k)` `implies (5)/(2)+1ltsqrt((25)/(4)-k)` `implies (25)/(4)-k gt(49)/(4)` `implies k lt - 6` Also , for these values of `k, (25)/(4)-k gt 0`. |
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