Please show all work so I can understand how to do it this is my last problem and I am stuck.

Please show all work so I can understand how to do it this is my last problem and I am stuck.

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I differ from the above answers on the following points----

I take up only those points where my answers are different.

Verities are --- (-2,5). , (-2,1)

Foci are --- (-2,8). , (-2,-2)

Asymptotes ----- y= -4x/3. +1/3

y= 4x/3+17/3

First, we have to understand what the parts of the equation represent, and how it relates to the given problem.

GENERAL EQUATION OF A VERTICAL HYPERBOLA:

(y-k)^{2}/a^{2} - (x-h)^{2}/b^{2} = 1

vertices: a^{2} = 16 -> a = ±4

b2 = 9 -> b = ±3

to find c^{2}: c^{2} = a^{2} + b^{2 }=> c^{2} = 16 + 9 => c^{2} = 25 => c = ± 5 => foci: (0,±c) => foci:(0,±5)

x-intercept: (±b,0) = (3,0),(-3,0)

center: (h,k) = in our case, is (-2,3). **Note, our x-coordinate of our center is -2 because x-(-2) = x+2**

latus rectum: 2b2/a = 2(9)/4 = 18/4 = 9/2

asymptotes: (y-3)^{2}/16 - (x+2)^{2}/9 = 0 => (y-3)^{2}/16 = (x+2)^{2}/9 => Next, cross-multiply to get 9(y-3)^{2}/9 = 16(x+2)^{2}/9 => (y-3)^{2} = 16(x+2)^{2}/9 => take the square root of both sides => y-3 = 4(x+2)/3=> add 3 to both sides to solve for y => y = [4(x+2)/3)+3]

Ok, so, now we have all the pieces of the puzzle to draw it!