Q87 / 180 · COMEDK 2017 · Mathematics

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
    $(0, \pm 5), \frac{32}{3}$
  • Correct answer
    C
    $(\pm 5,0), \frac{32}{3}$
  • D
    $(0, \pm 5), \frac{3}{32}$

Solution

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 $=\frac{2 b^{2}}{a}=\frac{32}{3}$

Hence, the correct answer is option: 'C'.

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