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

## Interactive practice questions

The graph of $x^2=4y$x2=4y has been plotted, along with points $A\left(4,4\right)$A(4,4) and $B\left(-6,9\right)$B(6,9). The point $F\left(0,1\right)$F(0,1) is called the focus and the line $y=-1$y=1 is called the directrix.

a

Determine the distance between points $A$A and $F$F.

b

Determine the perpendicular distance between point $A$A and the directrix.

c

Determine the distance between points $B$B and $F$F.

d

Determine the perpendicular distance between point $B$B and the directrix.

e

Complete the gaps to make the statement true.

The graph of $\left(\editable{}\right)^2=\editable{}$()2= represents the collection of points that are equidistant from the fixed point $($($\editable{}$, $\editable{}$$)$) and the fixed line $\editable{}$. The fixed point is called the focus and the fixed line is called the directrix.

Easy
Approx 5 minutes

The graph of $y^2=4x$y2=4x has been plotted, along with points $A\left(4,4\right)$A(4,4) and $B\left(9,-6\right)$B(9,6). The point $F\left(1,0\right)$F(1,0) is called the focus and the line $x=-1$x=1 is called the directrix.

Consider the parabola $x^2=16y$x2=16y.

Consider the parabola $x^2=16y$x2=16y.

### Outcomes

#### M8-1

Apply the geometry of conic sections

#### 91573

Apply the geometry of conic sections in solving problems