JEE Main & Advanced
Mathematics
Conic Sections
Question Bank
Hyperbola
question_answer
If e and e? are the eccentricities of the ellipse \[5{{x}^{2}}+9{{y}^{2}}=45\] and the hyperbola \[5{{x}^{2}}-4{{y}^{2}}=45\] respectively, then \[ee'=\] [EAMCET 2002]
A) 9
B) 4
C) 5
D) 1
Correct Answer:
D
Solution :
Clearly \[e=\frac{2}{3}\] and \[e'\] = \[A'N=a(1+\cos \theta )\], \[\therefore \]\[ee'\,=1.\]