Question

Which statements about the hyperbola are true? Check all that apply.

Answer 1

Answer:

Only option A is correct.

Step-by-step explanation:

From the given figure it is noticed that the vertices of hyperbola are (0,8) and (0,-8). It is a vertical hyperbola.

It means a=8.

From the rectangle we can say that the value of b is 6.

$c^2=a^2-b^2$

$c^2=(8)^2+(6)^2$

$c^2=100$

$c=10$

The focus of a vertical hyperbola are (0,c) and (0,-c). So, the focus of hyperbola are (0,10) and (0,-10).

Therefore option A is correct.

Asymptotes of a vertical hyperbola are

$y=\pm \frac{a}{b}x$

$y=\pm \frac{8}{6}x$

$y=\pm \frac{4}{3}x$

Directrix of a vertical hyperbola are

$y=\pm \frac{a^2}{c}$

$y=\pm \frac{(10)^2}{6}$

$y=\pm \frac{50}{3}$

Only option A is correct.