1.

If the foci of the ellipse `(x^(2))/(16)+(y^(2))/(b^(2))=1` and the hyperbola `(x^(2))/(144)-(y^(2))/(81)=(1)/(125)` coincide, the find the value of `b^(2)`.

Answer» Correct Answer - 7
For a hyperbola
`e^(2)=1+(b^(2))/(a^(2))=1+(81)/(144)=(225)/(144)`
`:. E = (15)/(12)=(5)/(4)`
Also, `a^(2)=(144)/(25)`
Hence, the foci are `(+- "ae", 0)-+(+-(12)/(5),(5)/(4))-=(+-3,0)`
Now, for an ellipse, ae = 3 or `a^(2)e^(2)=9`
Now, `b^(2)=a^(2)(1-e^(2))`
`rArr b^(2)=a^(2)-a^(2)e^(2)=16-9=7`


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