COMEDK · Maths · 15. Hyperbola
Find the coordinates of the foci and the length of the latusrectum of the hyperbol(a)
\(\frac{x^{2}}{9}-\frac{y^{2}}{16}=1\)
- A \((0, \pm 2), \frac{32}{3}\)
- B \((0, \pm 5), \frac{32}{3}\)
- C \((\pm 5,0), \frac{32}{3}\)
- D \((0, \pm 5), \frac{3}{32}\)
Answer & Solution
Correct Answer
(C) \((\pm 5,0), \frac{32}{3}\)
Step-by-step Solution
Detailed explanation
We have, \(a=3, b=4\) and \(c=\sqrt{a^{2}+b^{2}}=\sqrt{9+16}=5\) Therefore, the coordinates of the foci are \((\pm 5,0)\). Also, length of latusrectum \(=\frac{2 b^{2}}{a}=\frac{32}{3}\)
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