Question

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

A. There is a focus at (0,−10).

B. There is a focus at (0, 12).

C. y = x is an asymptote.

D. y = x is an asymptote.

E. x = is a directrix.

F. y = is a directrix.

Answer 1

the answers are B and E

Explanation:

Answer 2

Only option A is correct.

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 (a)/(b)x`

`y=\pm (8)/(6)x`

`y=\pm (4)/(3)x`

Directrix of a vertical hyperbola are

`y=\pm (a^2)/(c)`

`y=\pm ((10)^2)/(6)`

`y=\pm (50)/(3)`

Only option A is correct.