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# Parametric equation help... watch

1. Hi guys, so how do you sketch the circle using these parametric equations? And get the circle centre and the radius like in the mark scheme? Many thanks

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2. Try rearranging your x and y parametrics and using a trig identity
3. (Original post by sienna2266)
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Deriving the cartesian equation is one way, but unnecessary, particularly from the wording of the question.

You're told it's a circle.

Notice x oscillates about 1, with an amplitude of 2.
y oscillates about 3, again with an amplitude of 2.

So, centre is (1,3) and radius is 2....
4. (Original post by ghostwalker)
Deriving the cartesian equation is one way, but unnecessary, particularly from the wording of the question.

You're told it's a circle.

Notice x oscillates about 1, with an amplitude of 2.
y oscillates about 3, again with an amplitude of 2.

So, centre is (1,3) and radius is 2....
Thanks so much! so x values are between 3 and -1 and y values are between 5 and 1. so to work out the radius you do 3--1/2 = 2 or 5-1/2 =2 so radius = 2

But I am still confused with finding the centre
5. (Original post by sienna2266)
Thanks so much! so x values are between 3 and -1 and y values are between 5 and 1. so to work out the radius you do 3--1/2 = 2 or 5-1/2 =2 so radius = 2

But I am still confused with finding the centre
Centre is the point about which the coordinates oscillate.

Consider the x-coordinate. .

Cos varies between +/- 1, so the 2cos term varies +/- 2, whilst the 1 remains constant. i.e. the centre of the motion is x=1.

Note: the amplitude of the motion, i.e. the radius, is the multiplier on the cos or the sin term, i.e. 2, and you can read it off directly from the parameterization.
6. (Original post by ghostwalker)
Centre is the point about which the coordinates oscillate.

Consider the x-coordinate. .

Cos varies between +/- 1, so the 2cos term varies +/- 2, whilst the 1 remains constant. i.e. the centre of the motion is x=1.

Note: the amplitude of the motion, i.e. the radius, is the multiplier on the cos or the sin term, i.e. 2, and you can read it off directly from the parameterization.
Ohhh that makes sense!! Thank you so much

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