Question:medium

If the straight line \[ x+by+1=0 \] is a polar with respect to the circle \[ x^2+y^2-8x+10y-8=0, \] but not a tangent and not a chord, then all the values of \(b\) lie in the interval

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For a line \[ ax+by+c=0, \] compare its perpendicular distance from the centre with the radius: \[ \boxed{ \begin{aligned} d d=r &\Rightarrow \text{Tangent} d>r &\Rightarrow \text{Outside the circle} \end{aligned} } \]
Updated On: Jul 18, 2026
  • \((-\infty,-1)\)
  • \((-\infty,-\frac43)\cup(-\frac34,\infty)\)
  • \((-1,7)\)
  • \(\left(-\frac43,-\frac34\right)\)
Show Solution

The Correct Option is D

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