What is the equation of the hyperbola with vertices at (0,-4) and (0,4) and foci at (0,-6) and (0,6)?

Step-by-step explanation:

We are given equation of hyperbola

Vertices are (0,-4) (0,4)

we can use formula

vertices :  (h , k+a) and (h,k-a)

we can compare and find h , k and 'a'

we can add both equations

we get

now, we can find 'a'

now, we can use foci formula

foci: (h, k + c), (h, k - c)

we know that

so, we can solve for b

now, we can use standard equation of hyperbola

now, we can plug values

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step-by-step explanation:

option c) graph of line going through 1, 4 and 3, 10

step-by-step explanation:

let y equal to margo's coin collection

let x equal to number of years

at the begining x=0, y=1 → point=(x,y)→point=(0,1)

she adds 3 coins per year, then y=1+3x

at x=1, y=1+3(1)=1+3→y=4→point=(x,y)→point=(1,4)

at x=3, y=1+3(3)=1+9→y=10→point=(x,y)→point=(3,10)

the graph of line going through (1, 4) and (3, 10), then the option c is the correct.