New Zealand
Level 8 - NCEA Level 3

# Calculating eccentricity of conic sections

## Interactive practice questions

What is true about the eccentricity $e$e of a hyperbola?

The eccentricity is greater than 1.

A

The eccentricity is equal to 0.

B

The eccentricity is greater than 0 and less than 1.

C

The eccentricity is equal to 1.

D

The eccentricity is greater than 1.

A

The eccentricity is equal to 0.

B

The eccentricity is greater than 0 and less than 1.

C

The eccentricity is equal to 1.

D
Easy
Less than a minute

The point $P\left(-9,\frac{36}{5}\right)$P(9,365) lies on a conic section with a focus at $\left(12,0\right)$(12,0) and directrix at $x=\frac{75}{4}$x=754.

Find the eccentricity of the conic section.

Consider the hyperbola with the equation $16x^2-9y^2=144$16x29y2=144.

The point $P\left(\frac{17}{2},-\frac{45}{8}\right)$P(172,458) lies on a conic section with a focus at $\left(5,0\right)$(5,0) and directrix at $x=\frac{16}{5}$x=165.

Find the eccentricity of the conic section.

### Outcomes

#### M8-1

Apply the geometry of conic sections

#### 91573

Apply the geometry of conic sections in solving problems