How do you find the point where a parametric curve crosses the y-axis?

Set x=0, solve for t, then substitute into y.

How do you find a Cartesian equation from x=f(t), y=g(t)?

Make t the subject of one equation and substitute into the other.

Which identity eliminates \theta from x=a\sin\theta, y=b\cos\theta?

\sin^2\theta+\cos^2\theta=1, giving \frac{x^2}{a^2}+\frac{y^2}{b^2}=1.

Parametric form of a circle, centre (a, b), radius r?

x=a+r\cos\theta, y=b+r\sin\theta

What does the domain of t control?

Which part of the curve is drawn.

Parametric equationsEdexcel International A Level Maths: Flashcards

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What are parametric equations?

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What are parametric equations?: A pair $x=f(t)$ , $y=g(t)$ that give both coordinates in terms of a parameter.
Point at $t=-1$ on $x=3t-1$ , $y=t^2+2$ ?: $(-4,3)$
How do you find the point where a parametric curve crosses the y-axis?: Set $x=0$ , solve for $t$ , then substitute into $y$ .
How do you find a Cartesian equation from $x=f(t)$ , $y=g(t)$ ?: Make t the subject of one equation and substitute into the other.
Cartesian equation of $x=3t-1$ , $y=t^2+2$ ?: $y=\frac{(x+1)^2}{9}+2$
Cartesian equation of $x=2t$ , $y=\frac2t$ ?: $y=\frac4x$ , with $x\neq0$ .
Which identity eliminates $\theta$ from $x=a\sin\theta$ , $y=b\cos\theta$ ?: $\sin^2\theta+\cos^2\theta=1$ , giving $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ .
Cartesian equation of $x=2+3\sin\theta$ , $y=1+3\cos\theta$ ?: $(x-2)^2+(y-1)^2=9$
Parametric form of $y=x^2+1$ ?: $x=t$ , $y=t^2+1$
Parametric form of a circle, centre (a, b), radius r?: $x=a+r\cos\theta$ , $y=b+r\sin\theta$
What does the domain of t control?: Which part of the curve is drawn.
A ball has $x=20t$ , $y=15t-5t^2$ . When does it land?: When $y=0$ : $t=3$ .

Exam questions on Parametric equations

A curve $C$ has parametric equations $x=3t-1$ , $y=t^2+2$ , where $t$ is a real parameter.
Find the coordinates of the points where $C$ meets the line $y=11$ .2 marks
A curve $D$ has parametric equations $x=3\sin t$ , $y=2\cos t$ , for $0\leq t<2\pi$ .
Find the coordinates of the points where $D$ meets the $y$ -axis.2 marks
A ball is thrown so that, $t$ seconds later, its horizontal distance is $x=20t$ metres and its height is $y=15t-5t^2$ metres, for $t\geq0$ until it lands.
Find a Cartesian equation of the path of the ball, in the form $y=f(x)$ .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).