A) \[{{\tan }^{-1}}\,\sqrt{\frac{{{r}^{2}}-{{b}^{2}}}{{{a}^{2}}-{{r}^{2}}}}\]
B) \[{{\tan }^{-1}}\,\sqrt{\frac{{{r}^{2}}-{{a}^{2}}}{{{b}^{2}}-{{r}^{2}}}}\]
C) \[{{\tan }^{-1}}\,\sqrt{\frac{{{r}^{2}}-{{b}^{2}}}{{{r}^{2}}-{{a}^{2}}}}\]
D) \[{{\tan }^{-1}}\,\sqrt{\frac{{{r}^{2}}-{{a}^{2}}}{{{r}^{2}}-{{b}^{2}}}}\]
Correct Answer: A
Solution :
Let equation of circle is \[t=0\]. Tangent to ellipse is \[u=-6\,\,m{{s}^{-1}}\] If it is a tangent to the circle, then it is perpendicular form (0,0) is equal to radius. \[t=6\] \[v=6\,m{{s}^{-1}}\] \[W=\frac{1}{2}m{{v}^{2}}-\frac{1}{2}m{{u}^{2}}\Rightarrow \,W=0\] \[{{h}_{A}}<{{h}_{B}}\] \[{{d}_{A}}>{{d}_{B}}\] \[{{c}_{2}}\]You need to login to perform this action.
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