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Question

Let e1 and e2 are the eccentricities of 16x2+9y2=144 and 16x29y2=144 respectively, then which of the following is/are correct

A
e21+e22>3
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B
e21+e22<3
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C
e21e22>1
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D
1e21+le22>3
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Solution

The correct options are
A e21+e22>3
C e21e22>1
16x2+9y2=144x29+y216=1
a2=9, b2=16, b>a
e21=1a2b2=1916=716

16x29y2=144x29y216=1
a2=9, b2=16
e22=1+b2a2=1+169=259

e21+e22=716+259=463144>3

e21e22=716×259=175144>1

1e21+1e22=167+925=463175<3

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