WBJEE · Maths · Hyperbola
The equation of hyperbola whose coordinates of the foci are (±8,0) and the length of latusrectum is 24 units, is
- A \(3 x^{2}-y^{2}=48\)
- B \(4 x^{2}-y^{2}=48\)
- C \(x^{2}-3 y^{2}=48\)
- D \(x^{2}-4 y^{2}=48\)
Answer & Solution
Correct Answer
(A) \(3 x^{2}-y^{2}=48\)
Step-by-step Solution
Detailed explanation
Let equation of hyperbola be \[ \frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1 \] Given, foci, \((\pm 8,0)=(\pm a e, 0)\) \(\Rightarrow \quad a e=8\) and length of latusrectum \(=\frac{2 b^{2}}{a}\) \(\therefore\) \(24=\frac{2 b^{2}}{a}\) \(\Rightarrow \quad b^{2}=12 a\)…
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