A) \[{{a}^{2}}+{{b}^{2}}=14\]
B) there is a director circle of the hyperbola
C) centre of the director circle is (0, 0)
D) length of latusrectum of the hyperbola is
Correct Answer: D
Solution :
For the ellipse, a = 5 and \[e=\sqrt{\frac{25-9}{25}}=\frac{4}{5}\] \[\therefore \] \[ae=4\] Hence, the focii are (-4, 0) and (4, 0). For the hyperbola, ae = 4, e = 2 \[\therefore \] a = 2 \[{{b}^{2}}=4(4-1)=12\] \[b=\sqrt{12}\] Length of latusrectum \[=\frac{2{{b}^{2}}}{a}=2\times \frac{12}{2}\] \[=12\]You need to login to perform this action.
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