# Parametric Equations helpWatch

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#1
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.
Last edited by bhyvuoogyyu; 1 year ago
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1 year ago
#2
(Original post by 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.
For the first part, you want to elimiate the parameter somehow. Notice that you can rearrange the first equation to: and the second to So you can substitute the second equation now into the first and eliminate .
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1 year ago
#3
(Original post by 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.
Can you use brackets, please, to show us the equations as accurately as possible?

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.
1
1 year ago
#4
Can someone please help me out in part b of the question above, I’m struggling with it too...
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1 year ago
#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
0
1 year ago
#6
(Original post by 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
Got it! Thank you
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3 weeks ago
#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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3 weeks ago
#8
(Original post by 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
That's incorrect. Have a look at post #3. The orginal question is poorly ( and incorrectly) bracketed, so that's not the correct equation.

Post should have said: x=(1+4t)/(1-t) , y=(2+bt)/(1-t) and have a go from there.
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3 weeks ago
#9
can you show the working out because its vey confusing
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3 weeks ago
#10
(Original post by genius7277)
can you show the working out because its vey confusing
Fully worked solutions are against the forum rules, and I await a response from Carboxylic first of all.
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