Question

Which statements about the hyperbola are true? Check all that apply

Answer 1

Statements 1, 2 and 5 are true.

Explanation:

The following statements are true.

1. The center is located at (0,0) - clearly visible in the image.

2. The vertex is at (-6,0) - This is also true. If we see the left vertex, it lies between -4 and -8. Taking a half box scale, we can see that the vertex lies at -6,0 and the other vertex is at (6,0)

5. The directrices are vertical lines - This is true.

3. The transverse axis of the graph is horizontal here. The vertical line is the conjugate axis.

4. The foci are located within the rectangular reference box. This is not true. as its located outside the box.

Answer 2

we know that

statements
case a) the center is located at (0,0)?
the statement is true

case b) There is a vertex at (-6,0)?
the statement is true.
There is a vertex at (-6,0) and at (6,0)

case c) The transverse axis of the graphs is vertical
The statement is not true
The line joining the vertices is called the transverse axis and the line perpendicular to this is called the conjugate axis.
in this case the transverse axis is horizontal and the conjugate axis is vertical

case d) The foci are located within the rectangular reference box
The statement is not true
The foci are outside the rectangular reference box

case e)The directices are vertical lines
The statement is true