How to find the vertices of the hyperbole

(y - 3)²/9 - (x - 1)²/27 = 1

Step-by-step explanation:

1. Identify the centre of the hyperbola.

The centre is half-way between the two vertices.

((x₂ + x₁)/2, (y₂ + y₁)/2) = ((1 + 1)/2, (6 + 0)/2) = (2/2, 6/2) = (1, 3)

The centre is at (1, 3).

(1, 3) = (h, k), so

h = 1, k = 3

2. Identify the type of hyperbola.

Plot the vertices, foci, and centre.

We can see from Fig. 1 that we have a vertical hyperbola.

The equation for a vertical hyperbola is

(y - k)²/a² - (x - h)²/b² = 1

3. Identify the value of a

Count from the centre to either vertex.

a = 3

4. Identify the value of c.

Count from the centre to either focus.

c = 6

5. Identify the value of b

a² + b² =   c²

3² + b² =   6²

9 + b² = 36

Subtract 9 from each side

b² = 27

Take the square root of each side

b = √27

6. Write the equation for the hyperbola

We now have all the values needed: h, k, a, and b

The equation for the hyperbola is

(y - 3)²/9 - (x - 1)²/27 = 1

The graph of your hyperbola is shown in Fig. 2.

24

step-by-step explanation:

just sum

10 + 10 = 20