WBJEE · Maths · Hyperbola
The transverse axis of a hyperbola is along the \(x\) -axis and its length is \(2 a\). The vertex of the hyperbola bisects the line segment joining the centre and the focus. The equation of the hyperbola is
- A \(6 x^{2}-y^{2}=3 a^{2}\)
- B \(x^{2}-3 y^{2}=3 a^{2}\)
- C \(x^{2}-6 y^{2}=3 a^{2}\)
- D \(3 x^{2}-y^{2}=3 a^{2}\)
Answer & Solution
Correct Answer
(D) \(3 x^{2}-y^{2}=3 a^{2}\)
Step-by-step Solution
Detailed explanation
Let e be the eccentricity of hyperbola and length of conjugate axis be \(2 h\). since, vertex \((a, 0)\) bisects the join of centre (0,0) and focus \((a e, 0)\) \[ \begin{array}{l} a=\frac{a e+0}{2} \Rightarrow e=2 \\ b^{2}=a^{2}\left(c^{2}-1\right)=3 a^{2} \end{array} \]…
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