A) 4
B) \[10\]
C) \[-16\]
D) ±16
Correct Answer: C
Solution :
Equation of circle is \[4{{x}^{2}}+4{{y}^{2}}-8x+16y+k=0\] \[\therefore \] Radius of circle \[\sqrt{1+4-\frac{k}{4}}=\sqrt{5-\frac{k}{4}}\] According to the question, area of circle \[\pi {{r}^{2}}=9\pi \] \[\Rightarrow \] \[\pi \left( 5-\frac{k}{4} \right)=9\pi \] \[\Rightarrow \] \[5-\frac{k}{4}=9\] \[\Rightarrow \] \[\frac{k}{4}=-4\] \[\Rightarrow \] \[k=-16\]
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