Please help me with this one question from my Algebra homework that I have been stuck on for hours. Please help me as soon as possible please

Question

1.) Identify the value of p for the parabola.

A.) p = 20

B.) p = −5

C.) p = −20

D.) p = 5

2.) Identify the asymptotes of the hyperbola.

A.)

B.)

C.) y = 0, x = 0

D.)

Please help me

Answer 1

if the simple x=Ay² is examined for distance to focus from vertex (equal distance from vertex to directix),

at y₀=1/2A,,,,x=1/4A =-5 in this case, must go minus five units x from vertex to reach focus.which is the distance to focus from vertex (called p in thius problem). Vertex is at (8,-2), focus is at (3,-2). Some people consider p to be a distance always positive, and then p=5.

What I am doing in the above is setting up a square. At y=1/2A, the horizontal line through it is obviously perpendicular to directix Distance to directix to curve is 2p. Becuase of the definition of parabola that equals the distance from the foucs to the point.drawn parallel to the x-axis. (we have squaresince y=1/2A and pependicular side is 2*(1/4A)). Now 2p=1/2A. I did this at the origin because moving a curve does not change distance measurements between points. Look at solving 2x=y for square where x=Ay², or 2Ay²=y which is at y=1/2A

second question, method is to eliminate the 1 from the equation

This is a valid method because when x is large the values of y approach the assymptope. Remember+/-a=+/-b is same as a=+/-b. see y=+/-√[(x-a)²-1]+k is very much the same as y= +/-√[(x-a)²]+k= +/-(x-a)+k

Answer 2

let me do 1 for now then i'll re-edit once i do 2 unless someone else answers

this is a sideways parabola (check graph) and sideways parabolas have a general form:

x - h = 1/4p x (y - k)²

our sideways parabola looks like x - 8 = -1/20 x (y + 2)²

if we do some matching, we can see that h = 8, k = -2, and 1/4p = -1/20. This last equation is important bc it has the p we're looking for. So just solve for p in 1/4p = -1/20

ANSWER: -5

Edit: #2 is the same method as #1 but now we're working with a hyperbola. just find the general form of a hyperbola and do some matching to find your asymptotes. here's a helpful guide to doing so

https://useruploads.socratic.org/B6ETKfBRxqwsZ9PQdJUg_hyperbola-advanced-algebra-8-728.jpg

you can check your answer with me if u want