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.

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.

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

Directrix of a vertical hyperbola are

Only option A is correct.

g = (2, 2)

step-by-step explanation:

given the ratio is 1 : 1 then f is the midpoint of eg

let the coordinates of g = (x, y)

using the midpoint formula

(0 + x) = 1 ( multiply both sides by 2 )

0 + x = 2 ⇒ x = 2

similarly

(4 + y) = 3 ( multiply both sides by 2 )

4 + y = 6 ( subtract 4 from both sides )

y = 2

coordinates of g = (2, 2)

a: 1/6, j: 1/4

step-by-step explanation: you are welcome