Asap:
write an equation of hyperbola with foci at (-1, 1) and (5, 1) and vertices at (0, 1) and (4, 1)

The answer to your question is

Step-by-step explanation:

Data

Foci   (-1, 1) and (5, 1) [A and B]

Vertices (0, 1) and (4, 1)  [C and D]

See the image below. From the image we can conclude that it is a horizontal hyperbola.

Equation

From the image calculate the center

The center is in the middle of the vertices   (2, 1)

Now, calculate a, a is the distance from the center to the vertices, a = 2

Calculate c, c is the distance from the center to the foci, c = 3

Calculate b with the pythagorean theorem    c² = a² + b²

                                                                          b² = c² - a²

                                                                          b² = 3² - 2²

                                                                          b² = 9 - 4

                                                                          b² = 5

Substitution

option 2 is correct.

step-by-step explanation:

we are given two inequality equation

x+y> 5 and -3x+2y< -2

first we draw the graph of both function using t-table method

equation: x+y> 5

for x=0, y=5

for x=-5, y=0

table:

x   :   0     5

y   :   5     0

test point (0,0) , 0> 5

false

equation: -3x+2y< -2

for x=0, y=-1

for x=2, y=4

table:

x   :   0     2

y   : -1       4

test point (0,0) , 0< -2

true

now we draw the graph. see the attachment for graph.

common region would be solution set.

option 2 is correct.