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If the foci of the ellipse (x^(2))/(25)+...

If the foci of the ellipse `(x^(2))/(25)+(y^(2))/(b^(2))=1 ` and the hyperbola `(x^(2))/(144)-(y^(2))/(81)=(1)/(25)` coincide then the value of `b^(2)` is

Text Solution

Verified by Experts

Given hyperbola is
`(x^(2))/(144)-(y^(2))/(81)=(1)/(25)`
`"or "(x^(2))/(144//25)-(y^(2))/(81//25)=1`
So, foci of hyperbola are `(pmsqrt((144)/(25)+(81)/(25)),0)-=(pm3,0)`
These are foci of ellipse `(x^(2))/(16)+(y^(2))/(b^(2))=1` also.
`therefore" "3=sqrt(16-b^(2))`
`therefore" "b^(2)=7`
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