If the vertex of a hyperbola bisects the distance between its center and the correspoinding focus, then the ratio of the square of its conjugate axis

Question

If the vertex of a hyperbola bisects the distance between its center and the correspoinding focus, then the ratio of the square of its conjugate axis

If the vertex of a hyperbola bisects the distance between its center and the correspoinding focus, then the ratio of the square of its conjugate axis to the square of its transverse axis is 2 (b) 4 (c) 6 (d) 3
A. 2
B. 4
C. 6
D. 3

Monjur Alahi

5 views

2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Salim Ahmed Kawsar

Correct Answer - C
Let the hyperbola be
`(x^(2))/(a^(2))-(y^(2))/(b^(2))=1`
Then, 2a = ae, i.e., e = 2. Therefore,
`(b^(2))/(a^(2))=e^(2)-1=3`
`"or "((2b)^(2))/((2a)^(2))=3`

5 views Answered 2023-02-05 15:29