New Zealand
Level 8 - NCEA Level 3

# Applications of Circles

## Interactive practice questions

The radio tower on a navy vessel continuously sends out signals in every direction to pick up any other vessels within a $11$11 km radius.

Let the tower be positioned at $\left(0,0\right)$(0,0) on the plane.

a

A submarine is $9.1$9.1 km East and $7.1$7.1 km North of the tower. What is its direct distance from the tower?

b

Will the radio tower's signals pick up the submarine?

No

A

Yes

B

No

A

Yes

B
Easy
Approx 3 minutes

Consider a circle with centre $O$O at $\left(0,0\right)$(0,0) that passes through the point $A\left(-7,6\right)$A(7,6). A diameter is drawn from point $A$A to point $B$B on the circle.

State the coordinates of point $B$B.

Consider the diagram of the circle with centre $B$B and point $A$A$\left(3,3\right)$(3,3) on the circumference. $\triangle PAB$PAB is such that $PA$PA is a horizontal interval with $PA=4$PA=4 and $PB=5$PB=5.

A point $P$P$\left(x,y\right)$(x,y) moves so that it is always $7$7 units from the point $\left(0,0\right)$(0,0).

### Outcomes

#### M8-1

Apply the geometry of conic sections

#### 91573

Apply the geometry of conic sections in solving problems