Question

PLEASE HELP!
Question is attached bellow

Answer 1

`\sf \left(\boxed{1},\boxed{5}\right) \textsf{ and } \left(\boxed{-9},\boxed{5}\right)`

Explanation:

Given:

`((x+4)^2)/(25)-((y-5)^2)/(4)=1`

To find:

Coordinate of the vertices

Solution:

The given equation represents a hyperbola in standard form.

To find the coordinates of the vertices, we can compare it to the general equation for a hyperbola with a horizontal major axis:

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

In this case, we have:

`((x+4)^2)/(25)-((y-5)^2)/(4)=1`

We can see that the center of the hyperbola is at the point (-4, 5), which is represented by (h, k) in the general equation.

Now, we can determine the values of a and b:

a² = 25, so a = 5

b² = 4, so b = 2

The coordinates of the vertices are (h ± a, k), so for this hyperbola:

Vertices: (-4 ± 5, 5)

The two vertices are:

Vertex A: (-4 + 5, 5) = (1, 5)

Vertex B: (-4 - 5, 5) = (-9, 5)

So, the coordinates of the vertices of the hyperbola are:

`\sf \left(\boxed{1},\boxed{5}\right) \textsf{ and } \left(\boxed{-9},\boxed{5}\right)`