Convert more complex Parametric to Cartesian Equations: $x(t)=frac 3 2(t+frac 1 t),y(t)=2(t-frac 1 t)$...
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Trying to these functions into a cartesian equation:
$$x(t)=frac 3 2(t+frac 1 t),y(t)=2(t-frac 1 t)$$
parametric curves
asked Jan 2 at 11:47
anon101anon101
1
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closed as off-topic by Kavi Rama Murthy, José Carlos Santos, Nosrati, Lord_Farin, hardmath Jan 2 at 17:57
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Kavi Rama Murthy, José Carlos Santos, Nosrati, Lord_Farin, hardmath
If this question can be reworded to fit the rules in the help center, please edit the question.
add a comment |
$begingroup$
Trying to these functions into a cartesian equation:
$$x(t)=frac 3 2(t+frac 1 t),y(t)=2(t-frac 1 t)$$
parametric curves
asked Jan 2 at 11:47
anon101anon101
1
$endgroup$
closed as off-topic by Kavi Rama Murthy, José Carlos Santos, Nosrati, Lord_Farin, hardmath Jan 2 at 17:57
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Kavi Rama Murthy, José Carlos Santos, Nosrati, Lord_Farin, hardmath
If this question can be reworded to fit the rules in the help center, please edit the question.
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what did you try?
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– Martín Vacas Vignolo
Jan 2 at 11:50
add a comment |
$begingroup$
Trying to these functions into a cartesian equation:
$$x(t)=frac 3 2(t+frac 1 t),y(t)=2(t-frac 1 t)$$
parametric curves
asked Jan 2 at 11:47
anon101anon101
1
$endgroup$
Trying to these functions into a cartesian equation:
$$x(t)=frac 3 2(t+frac 1 t),y(t)=2(t-frac 1 t)$$
parametric curves
parametric curves
asked Jan 2 at 11:47
anon101anon101
1
asked Jan 2 at 11:47
anon101anon101
1
asked Jan 2 at 11:47
anon101anon101
1
asked Jan 2 at 11:47
anon101anon101
1
asked Jan 2 at 11:47
anon101anon101
1
1
closed as off-topic by Kavi Rama Murthy, José Carlos Santos, Nosrati, Lord_Farin, hardmath Jan 2 at 17:57
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Kavi Rama Murthy, José Carlos Santos, Nosrati, Lord_Farin, hardmath
If this question can be reworded to fit the rules in the help center, please edit the question.
closed as off-topic by Kavi Rama Murthy, José Carlos Santos, Nosrati, Lord_Farin, hardmath Jan 2 at 17:57
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Kavi Rama Murthy, José Carlos Santos, Nosrati, Lord_Farin, hardmath
If this question can be reworded to fit the rules in the help center, please edit the question.
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what did you try?
$endgroup$
– Martín Vacas Vignolo
Jan 2 at 11:50
add a comment |
$begingroup$
what did you try?
$endgroup$
– Martín Vacas Vignolo
Jan 2 at 11:50
$begingroup$
what did you try?
$endgroup$
– Martín Vacas Vignolo
Jan 2 at 11:50
$begingroup$
what did you try?
$endgroup$
– Martín Vacas Vignolo
Jan 2 at 11:50
add a comment |
3 Answers
3
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oldest
votes
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Note that $4=(t+1/t)^2-(t-1/t)^2=(2x/3)^2-(y/2)^2$.
answered Jan 2 at 11:51
J.G.J.G.
28.7k22845
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add a comment |
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Hint:
$$left(t+dfrac1tright)^2-left(t-dfrac1tright)^2=?$$
Alternatively WLOG put $t=tan rimplies t+dfrac1t=2csc2r,t-dfrac1t=?$
answered Jan 2 at 11:51
lab bhattacharjeelab bhattacharjee
226k15157275
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add a comment |
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we have $$frac{2}{3}x=t+frac{1}{t}$$
$$frac{y}{2}=t-frac{1}{t}$$ adding both equations we get
$$frac{2}{3}x+frac{1}{2}y=2t$$ now we can eliminate $t$
answered Jan 2 at 11:55
Dr. Sonnhard GraubnerDr. Sonnhard Graubner
76.8k42866
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Is there an easier way to eliminate t than subbing that bottom equation into one of the ones above?
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– anon101
Jan 2 at 22:06
add a comment |
3 Answers
3
active
oldest
votes
3 Answers
3
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Note that $4=(t+1/t)^2-(t-1/t)^2=(2x/3)^2-(y/2)^2$.
answered Jan 2 at 11:51
J.G.J.G.
28.7k22845
$endgroup$
add a comment |
$begingroup$
Note that $4=(t+1/t)^2-(t-1/t)^2=(2x/3)^2-(y/2)^2$.
answered Jan 2 at 11:51
J.G.J.G.
28.7k22845
$endgroup$
add a comment |
$begingroup$
Note that $4=(t+1/t)^2-(t-1/t)^2=(2x/3)^2-(y/2)^2$.
answered Jan 2 at 11:51
J.G.J.G.
28.7k22845
$endgroup$
Note that $4=(t+1/t)^2-(t-1/t)^2=(2x/3)^2-(y/2)^2$.
answered Jan 2 at 11:51
J.G.J.G.
28.7k22845
answered Jan 2 at 11:51
J.G.J.G.
28.7k22845
answered Jan 2 at 11:51
J.G.J.G.
28.7k22845
answered Jan 2 at 11:51
J.G.J.G.
28.7k22845
28.7k22845
add a comment |
add a comment |
$begingroup$
Hint:
$$left(t+dfrac1tright)^2-left(t-dfrac1tright)^2=?$$
Alternatively WLOG put $t=tan rimplies t+dfrac1t=2csc2r,t-dfrac1t=?$
answered Jan 2 at 11:51
lab bhattacharjeelab bhattacharjee
226k15157275
$endgroup$
add a comment |
$begingroup$
Hint:
$$left(t+dfrac1tright)^2-left(t-dfrac1tright)^2=?$$
Alternatively WLOG put $t=tan rimplies t+dfrac1t=2csc2r,t-dfrac1t=?$
answered Jan 2 at 11:51
lab bhattacharjeelab bhattacharjee
226k15157275
$endgroup$
add a comment |
$begingroup$
Hint:
$$left(t+dfrac1tright)^2-left(t-dfrac1tright)^2=?$$
Alternatively WLOG put $t=tan rimplies t+dfrac1t=2csc2r,t-dfrac1t=?$
answered Jan 2 at 11:51
lab bhattacharjeelab bhattacharjee
226k15157275
$endgroup$
Hint:
$$left(t+dfrac1tright)^2-left(t-dfrac1tright)^2=?$$
Alternatively WLOG put $t=tan rimplies t+dfrac1t=2csc2r,t-dfrac1t=?$
answered Jan 2 at 11:51
lab bhattacharjeelab bhattacharjee
226k15157275
answered Jan 2 at 11:51
lab bhattacharjeelab bhattacharjee
226k15157275
answered Jan 2 at 11:51
lab bhattacharjeelab bhattacharjee
226k15157275
answered Jan 2 at 11:51
lab bhattacharjeelab bhattacharjee
226k15157275
226k15157275
add a comment |
add a comment |
$begingroup$
we have $$frac{2}{3}x=t+frac{1}{t}$$
$$frac{y}{2}=t-frac{1}{t}$$ adding both equations we get
$$frac{2}{3}x+frac{1}{2}y=2t$$ now we can eliminate $t$
answered Jan 2 at 11:55
Dr. Sonnhard GraubnerDr. Sonnhard Graubner
76.8k42866
$endgroup$
$begingroup$
Is there an easier way to eliminate t than subbing that bottom equation into one of the ones above?
$endgroup$
– anon101
Jan 2 at 22:06
add a comment |
$begingroup$
we have $$frac{2}{3}x=t+frac{1}{t}$$
$$frac{y}{2}=t-frac{1}{t}$$ adding both equations we get
$$frac{2}{3}x+frac{1}{2}y=2t$$ now we can eliminate $t$
answered Jan 2 at 11:55
Dr. Sonnhard GraubnerDr. Sonnhard Graubner
76.8k42866
$endgroup$
$begingroup$
Is there an easier way to eliminate t than subbing that bottom equation into one of the ones above?
$endgroup$
– anon101
Jan 2 at 22:06
add a comment |
$begingroup$
we have $$frac{2}{3}x=t+frac{1}{t}$$
$$frac{y}{2}=t-frac{1}{t}$$ adding both equations we get
$$frac{2}{3}x+frac{1}{2}y=2t$$ now we can eliminate $t$
answered Jan 2 at 11:55
Dr. Sonnhard GraubnerDr. Sonnhard Graubner
76.8k42866
$endgroup$
we have $$frac{2}{3}x=t+frac{1}{t}$$
$$frac{y}{2}=t-frac{1}{t}$$ adding both equations we get
$$frac{2}{3}x+frac{1}{2}y=2t$$ now we can eliminate $t$
answered Jan 2 at 11:55
Dr. Sonnhard GraubnerDr. Sonnhard Graubner
76.8k42866
answered Jan 2 at 11:55
Dr. Sonnhard GraubnerDr. Sonnhard Graubner
76.8k42866
answered Jan 2 at 11:55
Dr. Sonnhard GraubnerDr. Sonnhard Graubner
76.8k42866
answered Jan 2 at 11:55
Dr. Sonnhard GraubnerDr. Sonnhard Graubner
76.8k42866
76.8k42866
$begingroup$
Is there an easier way to eliminate t than subbing that bottom equation into one of the ones above?
$endgroup$
– anon101
Jan 2 at 22:06
add a comment |
$begingroup$
Is there an easier way to eliminate t than subbing that bottom equation into one of the ones above?
$endgroup$
– anon101
Jan 2 at 22:06
$begingroup$
Is there an easier way to eliminate t than subbing that bottom equation into one of the ones above?
$endgroup$
– anon101
Jan 2 at 22:06
$begingroup$
Is there an easier way to eliminate t than subbing that bottom equation into one of the ones above?
$endgroup$
– anon101
Jan 2 at 22:06
add a comment |
$begingroup$
what did you try?
$endgroup$
– Martín Vacas Vignolo
Jan 2 at 11:50