Which is the equation of a hyperbola centered at the origin with vertex (0,sqrt12) that passes through (2sqrt3,6)a. y^2/36-x^2/12=1b. y^2/12-x^2/36=1c. y^2/6-x^2/12=1d. y^2/12-x^2/6=1

D.

Step-by-step explanation:

we are given

we can use standard equation of hyperbola

where

center=(h,k)

center at origin

so, h=0 and k=0

vertex is

we can use formula

vertices: (h, k + a)

we get

we can plug k=0

now, we can plug these values

now, we are given it passes through

so, we have

we can plug these values and then we can solve for b

and we get

we can solve for b

and we get

now, we can plug these values

we can simplify it

and we get

answer: the distance

step-by-step explanation:

to calculate the distance d of a line segment with endpoints (x1, y1) and (x2, y2) use the formula d (x2 x1)2 (y2 y1)2. to calculate the midpoint of a line segment with endpoints (x1, y1) and (x2, y2) use the formula