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The ellipse (x^(2))/(25)+(y^(2))/(16)=1 ...

The ellipse `(x^(2))/(25)+(y^(2))/(16)=1` and the hyperbola `(x^(2))/(25)-(y^(2))/(16) =1` have in common

A

A. centre and vertices only

B

B. centre, foci and vertices

C

C. centre, foci and directrices

D

D. centre only

Text Solution

Verified by Experts

The correct Answer is:
A
For ellipse `(x^(2))/(25) + (y^(2))/(16) =1, a = 5` and `b = 4`
For hyperbola `(x^(2))/(25) - (y^(2))/(16) =1, a = 5` and `b = 4`
For ellipse `a^(2)e^(2) = a^(2)-b^(2) = 25 - 16 =9`
For hyperbola `a^(2)e^(2) = a^(2)+b^(2) = 25 + 16 = 41`
`:.` center and vertices only are common.
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