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Stage 4 - Stage 5

The graph of $x^2=4y$`x`2=4`y` 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.

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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 $y^2=4x$`y`2=4`x` 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 $x^2=16y$`x`2=16`y`.

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

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