# Parametric Equations help

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bhyvuoogyyu

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hey i need a hand with this Parametric Equations question

C has parametric equations x=1+4t/1-t , y=2+bt/1-t , -1≤t≤ 0

a)Show that the Cartesian equation of C is y=(2+b/5)x+(8-b/5),over an appropriate domain.

Given that C is a line segment and that the gradient of the line is −1,

b)show that the length of the line segment is a√2 , where a is a rational number to be found.

I've not really got any clue where to start thanks in advance.

C has parametric equations x=1+4t/1-t , y=2+bt/1-t , -1≤t≤ 0

a)Show that the Cartesian equation of C is y=(2+b/5)x+(8-b/5),over an appropriate domain.

Given that C is a line segment and that the gradient of the line is −1,

b)show that the length of the line segment is a√2 , where a is a rational number to be found.

I've not really got any clue where to start thanks in advance.

Last edited by bhyvuoogyyu; 3 years ago

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RDKGames

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(Original post by

hey i need a hand with this Parametric Equations question

C has parametric equations x=1+4t/1-t , y=2+bt/1-t , -1≤t≤ 0

a)Show that the Cartesian equation of C is y=(2+b/5)x+(8-b/5),over an appropriate domain.

Given that C is a line segment and that the gradient of the line is −1,

b)show that the length of the line segment is a√2 , where a is a rational number to be found.

I've not really got any clue where to start thanks in advance.

**bhyvuoogyyu**)hey i need a hand with this Parametric Equations question

C has parametric equations x=1+4t/1-t , y=2+bt/1-t , -1≤t≤ 0

a)Show that the Cartesian equation of C is y=(2+b/5)x+(8-b/5),over an appropriate domain.

Given that C is a line segment and that the gradient of the line is −1,

b)show that the length of the line segment is a√2 , where a is a rational number to be found.

I've not really got any clue where to start thanks in advance.

and the second to

So you can substitute the second equation now into the first and eliminate .

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begbie68

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**bhyvuoogyyu**)

hey i need a hand with this Parametric Equations question

C has parametric equations x=1+4t/1-t , y=2+bt/1-t , -1≤t≤ 0

a)Show that the Cartesian equation of C is y=(2+b/5)x+(8-b/5),over an appropriate domain.

Given that C is a line segment and that the gradient of the line is −1,

b)show that the length of the line segment is a√2 , where a is a rational number to be found.

I've not really got any clue where to start thanks in advance.

RDK thinks you mean

x = 1 + 4t/(1-t)

but I have an inkling that you intended

x = (1+4t) / (1-t)

although you have actually written

x = 1 +(4t/1) - t

... and similarly for the y-equations.

Whichever it might be, RDK's method is correct.

Cartesian Eqn means ONLY in terms of x and y, so eliminate t from the equations by substitution. (this is similar to similtaneous eqn processes)

If you manage this, you should get

y = (2+b)x / 5 + (8-b) / 5

Then you need to consider only the small part of this straight line as determined by the allowed values for t.

Think about how the limited values for t will limit the values for x and y/

[this is the hardest part of the question]

Once you have those limits, you'll easily see / calculate the length of the line segment.

Let us know how you get on.

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Ms_nnenna_

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#4

Can someone please help me out in part b of the question above, I’m struggling with it too...

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begbie68

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#5

as t changes from -1 to 0, that determines the set of possible values for x and also for y

sub these in to the cartesian equation and you can see that we've got a line segment (part of a straight line)

so you can then calculate the length of that line segment

sub these in to the cartesian equation and you can see that we've got a line segment (part of a straight line)

so you can then calculate the length of that line segment

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Ms_nnenna_

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(Original post by

as t changes from -1 to 0, that determines the set of possible values for x and also for y

sub these in to the cartesian equation and you can see that we've got a line segment (part of a straight line)

so you can then calculate the length of that line segment

**begbie68**)as t changes from -1 to 0, that determines the set of possible values for x and also for y

sub these in to the cartesian equation and you can see that we've got a line segment (part of a straight line)

so you can then calculate the length of that line segment

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Carboxylic

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#7

I am substituting equation 1 into 2 so it is (x-1)/4 = (y-2)/b but after rearranging i cant get to the answer

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ghostwalker

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(Original post by

I am substituting equation 1 into 2 so it is (x-1)/4 = (y-2)/b but after rearranging i cant get to the answer

**Carboxylic**)I am substituting equation 1 into 2 so it is (x-1)/4 = (y-2)/b but after rearranging i cant get to the answer

Post should have said: x=(1+4t)/(1-t) , y=(2+bt)/(1-t) and have a go from there.

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genius7277

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ghostwalker

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(Original post by

can you show the working out because its vey confusing

**genius7277**)can you show the working out because its vey confusing

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jessiepip

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#11

I'm stuck on the same question please could you give me some direction as to what i should do

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ghostwalker

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(Original post by

I'm stuck on the same question please could you give me some direction as to what i should do

**jessiepip**)I'm stuck on the same question please could you give me some direction as to what i should do

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