Vertex and axis of y^2=4ax?

Vertex (0,0); axis is the x-axis.

State the focus-directrix property.

Every point on the parabola is the same distance from the focus as from the directrix.

What do t and -t give?

Two points that are reflections in the x-axis.

y^2=12x: find a, the focus and the directrix.

a=3, focus (3,0), directrix x=-3.

The parabolaEdexcel International A Level Further Maths: Flashcards

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Standard equation of the parabola in IAL FP1?

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Standard equation of the parabola in IAL FP1?: $y^2=4ax$
Focus of $y^2=4ax$ ?: $(a,0)$
Directrix of $y^2=4ax$ ?: $x=-a$
Parametric form of $y^2=4ax$ ?: $x=at^2,\ y=2at$
Vertex and axis of $y^2=4ax$ ?: Vertex $(0,0)$ ; axis is the $x$ -axis.
State the focus-directrix property.: Every point on the parabola is the same distance from the focus as from the directrix.
Distance $SP$ for $P(at^2,2at)$ ?: $a(t^2+1)$
Distance from $P(x,y)$ on $y^2=4ax$ to the directrix?: $x+a$
What does $t=0$ give?: The vertex $(0,0)$ .
What do $t$ and $-t$ give?: Two points that are reflections in the $x$ -axis.
$y^2=12x$ : find $a$ , the focus and the directrix.: $a=3$ , focus $(3,0)$ , directrix $x=-3$ .
Show $(at^2,2at)$ lies on $y^2=4ax$ .: $(2at)^2=4a^2t^2=4a(at^2)$ .

Exam questions on The parabola

The parabola $C$ has equation $y^2=12x$ . Its focus is $S$ .
The point $P(12,12)$ lies on $C$ . Use the focus-directrix property to find the distance $SP$ .2 marks
The parabola $C$ has equation $y^2=8x$ . A general point on $C$ has coordinates $(2t^2,4t)$ , where $t$ is a parameter.
The point $Q(50,-20)$ lies on $C$ . Find the value of $t$ at $Q$ .2 marks
The parabola $C$ has equation $y^2=16x$ , focus $S$ and directrix $l$ . The point $P(4t^2,8t)$ lies on $C$ .
Show that the distance $SP$ is equal to the perpendicular distance from $P$ to the directrix.3 marks

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Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).