第16章 16.9

(1)

$x^2 + 4y^2 = 4 \qquad \frac{x^2}{4} + y^2 = 1$

$\sqrt{4-1} = \sqrt{3}\text{から}$

焦点は$(\pm\sqrt{3}, 0)$

(2)

$9x^2 + 16y^2 = 144 \qquad \frac{x^2}{16} + \frac{y^2}{9} = 1$

$\sqrt{16-9} = \sqrt{7}\text{から}$

焦点は$(\pm\sqrt{7}, 0)$

(3)

$2x^2 + 3y^2 = 6 \qquad \frac{x^2}{3} + \frac{y^2}{2} = 1$

$\sqrt{3-2} = 1\text{から}$

焦点は$(\pm 1, 0)$

(4)

$8x^2 + 4y^2 - 16 = 0 \qquad \frac{x^2}{2} + \frac{y^2}{4} = 1$

$\sqrt{4-2} = \sqrt{2}\text{から}$

焦点は$(0, \pm\sqrt{2})$