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How to find PDE of all planes with the following condition [closed]
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Can someone help with the following problem :
Find the partial differential equation of all planes which are at a constant distance $a$ from the origin.
Thanks in advance for your time.
pde
asked Jul 27 at 14:19
learner
3,27731960
closed as off-topic by Dylan, mathreadler, amWhy, Adrian Keister, Xander Henderson Jul 29 at 0:53
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 improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Dylan, mathreadler, amWhy, Adrian Keister, Xander Henderson
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up vote
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Can someone help with the following problem :
Find the partial differential equation of all planes which are at a constant distance $a$ from the origin.
Thanks in advance for your time.
pde
asked Jul 27 at 14:19
learner
3,27731960
closed as off-topic by Dylan, mathreadler, amWhy, Adrian Keister, Xander Henderson Jul 29 at 0:53
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 improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Dylan, mathreadler, amWhy, Adrian Keister, Xander Henderson
I really have no clue what it means by "partial differential equation of all planes".........................
– Chee Han
Jul 27 at 22:58
I voted to close the question as off-topic. You might want to include more context, such as what kind of PDE you want to obtain (linear or not, how many unknown variables, etc), what form of the equation the solution will take (is it $z = f(x,y)$ or $F(x,y,z)=c$, etc), and what attempts have you made and your thoughts on the problem.
– Dylan
Jul 28 at 8:55
add a comment |Â
up vote
0
down vote
favorite
up vote
0
down vote
favorite
Can someone help with the following problem :
Find the partial differential equation of all planes which are at a constant distance $a$ from the origin.
Thanks in advance for your time.
pde
asked Jul 27 at 14:19
learner
3,27731960
Can someone help with the following problem :
Find the partial differential equation of all planes which are at a constant distance $a$ from the origin.
Thanks in advance for your time.
pde
asked Jul 27 at 14:19
learner
3,27731960
edited Jul 27 at 17:40
asked Jul 27 at 14:19
learner
3,27731960
asked Jul 27 at 14:19
learner
3,27731960
asked Jul 27 at 14:19
learner
3,27731960
3,27731960
closed as off-topic by Dylan, mathreadler, amWhy, Adrian Keister, Xander Henderson Jul 29 at 0:53
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 improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Dylan, mathreadler, amWhy, Adrian Keister, Xander Henderson
closed as off-topic by Dylan, mathreadler, amWhy, Adrian Keister, Xander Henderson Jul 29 at 0:53
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 improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Dylan, mathreadler, amWhy, Adrian Keister, Xander Henderson
I really have no clue what it means by "partial differential equation of all planes".........................
– Chee Han
Jul 27 at 22:58
I voted to close the question as off-topic. You might want to include more context, such as what kind of PDE you want to obtain (linear or not, how many unknown variables, etc), what form of the equation the solution will take (is it $z = f(x,y)$ or $F(x,y,z)=c$, etc), and what attempts have you made and your thoughts on the problem.
– Dylan
Jul 28 at 8:55
add a comment |Â
I really have no clue what it means by "partial differential equation of all planes".........................
– Chee Han
Jul 27 at 22:58
I voted to close the question as off-topic. You might want to include more context, such as what kind of PDE you want to obtain (linear or not, how many unknown variables, etc), what form of the equation the solution will take (is it $z = f(x,y)$ or $F(x,y,z)=c$, etc), and what attempts have you made and your thoughts on the problem.
– Dylan
Jul 28 at 8:55
I really have no clue what it means by "partial differential equation of all planes".........................
– Chee Han
Jul 27 at 22:58
I really have no clue what it means by "partial differential equation of all planes".........................
– Chee Han
Jul 27 at 22:58
I voted to close the question as off-topic. You might want to include more context, such as what kind of PDE you want to obtain (linear or not, how many unknown variables, etc), what form of the equation the solution will take (is it $z = f(x,y)$ or $F(x,y,z)=c$, etc), and what attempts have you made and your thoughts on the problem.
– Dylan
Jul 28 at 8:55
I voted to close the question as off-topic. You might want to include more context, such as what kind of PDE you want to obtain (linear or not, how many unknown variables, etc), what form of the equation the solution will take (is it $z = f(x,y)$ or $F(x,y,z)=c$, etc), and what attempts have you made and your thoughts on the problem.
– Dylan
Jul 28 at 8:55
add a comment |Â
1 Answer
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Let the required equation of the plane be $$z=lx+my+n\lx+my-z+n=0.....(1)$$Now the plane $(1)$ is at constant distance $a$ from the origin$$therefore a=fracsqrtl^2+m^2+1$$$$implies a=fracpm nsqrtl^2+m^2+1$$$$mboxHere p=fracsqrta^2+b^2+c^2$$$$implies n=fracpm nsqrtl^2+m^2+1$$$therefore (1) $ becomes$$lx+my-zpm asqrtl^2+m^2+1=0.....(2)$$Differentiating $(2)$ with respect to $x$ and $y$, we get$$l-fracdzdx=0mbox and m-fracdzdy=0$$or$$p=lmbox and q=m$$$$therefore(2)mbox reduces to $$$$px+qy-zpm asqrtp^2+q^2+1=0$$$$implies z=px+qypm sqrtp^2+q^2+1mbox is the required differential equation$$
answered Jul 28 at 16:59
Key Flex
4,015423
What are $p$ and $q$ here?
– Chee Han
Jul 28 at 21:20
add a comment |Â
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
0
down vote
accepted
Let the required equation of the plane be $$z=lx+my+n\lx+my-z+n=0.....(1)$$Now the plane $(1)$ is at constant distance $a$ from the origin$$therefore a=fracsqrtl^2+m^2+1$$$$implies a=fracpm nsqrtl^2+m^2+1$$$$mboxHere p=fracsqrta^2+b^2+c^2$$$$implies n=fracpm nsqrtl^2+m^2+1$$$therefore (1) $ becomes$$lx+my-zpm asqrtl^2+m^2+1=0.....(2)$$Differentiating $(2)$ with respect to $x$ and $y$, we get$$l-fracdzdx=0mbox and m-fracdzdy=0$$or$$p=lmbox and q=m$$$$therefore(2)mbox reduces to $$$$px+qy-zpm asqrtp^2+q^2+1=0$$$$implies z=px+qypm sqrtp^2+q^2+1mbox is the required differential equation$$
answered Jul 28 at 16:59
Key Flex
4,015423
What are $p$ and $q$ here?
– Chee Han
Jul 28 at 21:20
add a comment |Â
up vote
0
down vote
accepted
Let the required equation of the plane be $$z=lx+my+n\lx+my-z+n=0.....(1)$$Now the plane $(1)$ is at constant distance $a$ from the origin$$therefore a=fracsqrtl^2+m^2+1$$$$implies a=fracpm nsqrtl^2+m^2+1$$$$mboxHere p=fracsqrta^2+b^2+c^2$$$$implies n=fracpm nsqrtl^2+m^2+1$$$therefore (1) $ becomes$$lx+my-zpm asqrtl^2+m^2+1=0.....(2)$$Differentiating $(2)$ with respect to $x$ and $y$, we get$$l-fracdzdx=0mbox and m-fracdzdy=0$$or$$p=lmbox and q=m$$$$therefore(2)mbox reduces to $$$$px+qy-zpm asqrtp^2+q^2+1=0$$$$implies z=px+qypm sqrtp^2+q^2+1mbox is the required differential equation$$
answered Jul 28 at 16:59
Key Flex
4,015423
What are $p$ and $q$ here?
– Chee Han
Jul 28 at 21:20
add a comment |Â
up vote
0
down vote
accepted
up vote
0
down vote
accepted
Let the required equation of the plane be $$z=lx+my+n\lx+my-z+n=0.....(1)$$Now the plane $(1)$ is at constant distance $a$ from the origin$$therefore a=fracsqrtl^2+m^2+1$$$$implies a=fracpm nsqrtl^2+m^2+1$$$$mboxHere p=fracsqrta^2+b^2+c^2$$$$implies n=fracpm nsqrtl^2+m^2+1$$$therefore (1) $ becomes$$lx+my-zpm asqrtl^2+m^2+1=0.....(2)$$Differentiating $(2)$ with respect to $x$ and $y$, we get$$l-fracdzdx=0mbox and m-fracdzdy=0$$or$$p=lmbox and q=m$$$$therefore(2)mbox reduces to $$$$px+qy-zpm asqrtp^2+q^2+1=0$$$$implies z=px+qypm sqrtp^2+q^2+1mbox is the required differential equation$$
answered Jul 28 at 16:59
Key Flex
4,015423
Let the required equation of the plane be $$z=lx+my+n\lx+my-z+n=0.....(1)$$Now the plane $(1)$ is at constant distance $a$ from the origin$$therefore a=fracsqrtl^2+m^2+1$$$$implies a=fracpm nsqrtl^2+m^2+1$$$$mboxHere p=fracsqrta^2+b^2+c^2$$$$implies n=fracpm nsqrtl^2+m^2+1$$$therefore (1) $ becomes$$lx+my-zpm asqrtl^2+m^2+1=0.....(2)$$Differentiating $(2)$ with respect to $x$ and $y$, we get$$l-fracdzdx=0mbox and m-fracdzdy=0$$or$$p=lmbox and q=m$$$$therefore(2)mbox reduces to $$$$px+qy-zpm asqrtp^2+q^2+1=0$$$$implies z=px+qypm sqrtp^2+q^2+1mbox is the required differential equation$$
answered Jul 28 at 16:59
Key Flex
4,015423
edited Jul 28 at 21:49
answered Jul 28 at 16:59
Key Flex
4,015423
answered Jul 28 at 16:59
Key Flex
4,015423
answered Jul 28 at 16:59
Key Flex
4,015423
4,015423
What are $p$ and $q$ here?
– Chee Han
Jul 28 at 21:20
add a comment |Â
What are $p$ and $q$ here?
– Chee Han
Jul 28 at 21:20
What are $p$ and $q$ here?
– Chee Han
Jul 28 at 21:20
What are $p$ and $q$ here?
– Chee Han
Jul 28 at 21:20
add a comment |Â
I really have no clue what it means by "partial differential equation of all planes".........................
– Chee Han
Jul 27 at 22:58
I voted to close the question as off-topic. You might want to include more context, such as what kind of PDE you want to obtain (linear or not, how many unknown variables, etc), what form of the equation the solution will take (is it $z = f(x,y)$ or $F(x,y,z)=c$, etc), and what attempts have you made and your thoughts on the problem.
– Dylan
Jul 28 at 8:55