Parametric help

A curve c has parametric equations x=sec^2(t)+1, y=2sin(t), -pi/4<=t<=pi/4
Show that a Cartesian equation of c is y=√[(8-4x)/(1-x)] for a suitable domain which should be stated.

How do you rearrange this?

Reply 1

bongamin12

OP

2

A curve c has parametric equations x=sec^2(t)+1, y=2sin(t), -pi/4<=t<=pi/4
Show that a Cartesian equation of c is y=√[(8-4x)/(1-x)] for a suitable domain which should be stated.
How do you rearrange this?

Original post by bongamin12

A curve c has parametric equations x=sec^2(t)+1, y=2sin(t), -pi/4<=t<=pi/4
Show that a Cartesian equation of c is y=√[(8-4x)/(1-x)] for a suitable domain which should be stated.
How do you rearrange this?

Note that

\sec^2 t

can be written in terms of

\cos^2 t

, which can be written in terms of

\sin^2 t

, which can be written in terms of

y

. Hence eliminating the paramter

t

between the two equations.

Reply 3

bongamin12

OP

2

Original post by RDKGames

Note that

\sec^2 t

can be written in terms of

\cos^2 t

, which can be written in terms of

\sin^2 t

, which can be written in terms of

y

. Hence eliminating the paramter

t

between the two equations.

I've tried rearranging for cos^2(t)+sin^2(t) = 1 which got me:
(1/x-1)+(y/2)^2=1
However i rearragned this to get y=√[(4x-8)/(x-1)]

Original post by bongamin12

I've tried rearranging for cos^2(t)+sin^2(t) = 1 which got me:
(1/x-1)+(y/2)^2=1
However i rearragned this to get y=√[(4x-8)/(x-1)]

Same thing. Note that

\dfrac{a}{b} = \dfrac{-a}{-b}

.

Reply 5

bongamin12

OP

2

Original post by RDKGames

Same thing. Note that

\dfrac{a}{b} = \dfrac{-a}{-b}

.

Oh I should've been writing 1 as (-x-1)/(-x-1) correct ?

Original post by bongamin12

Oh I should've been writing 1 as (-x-1)/(-x-1) correct ?

No what I mean is that

\dfrac{4x-8}{x-1} = \dfrac{-(4x-8)}{-(x-1)}

Reply 7

bongamin12

OP

2

Original post by RDKGames

No what I mean is that

\dfrac{4x-8}{x-1} = \dfrac{-(4x-8)}{-(x-1)}

Oh ok I understand now. because it is a common factor.Thank you for the help ! I'll remember to look out for common factors better next time.

Reply 8

David Getling

19

Two general points. To be well prepared to tackle parametric equations you need to be very good at working with trig identities. Most students struggle quite a bit with these, so LOTS of practice with them is essential.

When you are asked to sketch a parametric curve, having a graphics display calculator can be a real godsend. Both the Casio fx-cg50 and the TI-Nspire CX will do a great job. They will also really help in many others ways that have nothing to do with graphs (eg. finding critical regions for hypothesis testing with binomial distributions).

Parametric help

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