A) \[4\pi (2-\sqrt{2})\]
B) \[8\pi (3-2\sqrt{2})\]
C) \[4\pi (3+\sqrt{2})\]
D) \[8\pi (2-\sqrt{2})\]
Correct Answer: B
Solution :
Equation of circle is \[{{(x-1)}^{2}}+{{(y-2)}^{2}}+\lambda (x-y+1)=0\] \[\Rightarrow \]\[{{x}^{2}}+{{y}^{2}}+x(\lambda -2)+y(-4-\lambda )+(5+\lambda )=0\] As cirlce touches x axis then \[{{g}^{2}}-c=0\] \[\frac{{{(\lambda -2)}^{2}}}{4}=(5+\lambda )\] \[{{\lambda }^{2}}+4-4\lambda =20+4\lambda \] \[{{\lambda }^{2}}-8\lambda -16=0\] \[\lambda =\frac{8\pm \sqrt{128}}{2}\] \[\lambda =4\pm 4\sqrt{2}\] \[Radius=\left| \frac{(-4-\lambda )}{2} \right|\] Put \[\lambda \]and get least radius.You need to login to perform this action.
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