NZ Level 8 (NZC) Level 3 (NCEA) [In development]
Applications of Ellipses

## Interactive practice questions

The equation $\frac{x^2}{324}+\frac{y^2}{289}=1$x2324+y2289=1 models the elliptical opening of a wind tunnel that is $36$36 metres wide and $34$34 metres high.

True or false?

True

A

False

B

True

A

False

B
Easy
Less than a minute

The orbit of Venus is an ellipse with the sun as one focus. Placing the centre of the ellipse at the origin, an approximate equation for the orbit is $\frac{x^2}{5017}+\frac{y^2}{4970}=1$x25017+y24970=1, where $x$x and $y$y are measured in millions of miles.

Find the greatest possible distance across the ellipse. Round your answer to the nearest million miles.

A cake maker has rectangular boxes measuring $40$40 cm in length and $20$20 cm in width. She often receives orders for cakes in the shape of an ellipse, and wants to determine the largest possible cake that can be made to fit inside the rectangular box.

The elliptical ceiling in a hall is $52$52 metres long and $8$8 metres tall.

### Outcomes

#### M8-1

Apply the geometry of conic sections

#### 91573

Apply the geometry of conic sections in solving problems