A) \[r>5\]
B) \[r>2\]
C) \[2<r<5\]
D) None of these
Correct Answer: C
Solution :
Standard equation of ellipse is \[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1\] where \[{{a}^{2}}>1,{{b}^{2}}>1\] \[\therefore \] \[\frac{{{x}^{2}}}{2-r}+\frac{{{y}^{2}}}{r-5}+1=0\] \[\Rightarrow \] \[\frac{{{x}^{2}}}{2-r}+\frac{{{y}^{2}}}{r-5}=-1\] \[\Rightarrow \] \[\frac{{{x}^{2}}}{r-2}+\frac{{{y}^{2}}}{5-r}=1\] \[\therefore \] \[r-2>0\]and \[5-r>0\] \[\Rightarrow \] \[r>2\]and \[r<5\] \[\Rightarrow \] \[2<r<5\]
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