NZ Level 8 (NZC) Level 3 (NCEA) [In development] Characteristics of hyperbolas

## Interactive practice questions

For any graph of a hyperbola, which of the following statements describe the locations of the foci, vertices, and centre with respect to one another? Select all that apply.

The foci are further from the centre than the vertices.

A

The centre is located at the midpoint of the two vertices.

B

The foci are closer to the centre than the vertices.

C

The centre is located at the midpoint of the two foci.

D

The foci are further from the centre than the vertices.

A

The centre is located at the midpoint of the two vertices.

B

The foci are closer to the centre than the vertices.

C

The centre is located at the midpoint of the two foci.

D
Easy
Approx 2 minutes

Determine whether the statement is true or false:

"The foci, vertices, and centre of a hyperbola all lie on the transverse axis."

The graph of $\frac{x^2}{16}-\frac{y^2}{9}=1$x216y29=1 is shown below.

The graph of $\frac{x^2}{9}-\frac{y^2}{16}=1$x29y216=1 is shown below.

### Outcomes

#### M8-1

Apply the geometry of conic sections

#### 91573

Apply the geometry of conic sections in solving problems