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`

Explanation

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`.