Polar Coordinates: Writing x^2+y^2+5x=0, x^2(x^2+y^2)=7y^2 as Values of R

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13whispers

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Write each equation in polar coordinates. Express as a function of t. Assume that r>0.

x^2+y^2+5x=0

x^2(x^2+y^2)=7y^2
 
13whispers said:
Write each equation in polar coordinates. Express as a function of t. Assume that r>0.

x^2+y^2+5x=0

x^2(x^2+y^2)=7y^2
Click to expand...
For problem (1) - rewrite as:

(x + 5/2)2 + y2 = (5/2)2

Continue.......
 
13whispers said:
Write each equation in polar coordinates. Express as a function of t. Assume that r>0.

x^2+y^2+5x=0

x^2(x^2+y^2)=7y^2
Click to expand...

Sometimes there are shortcuts for this process, but in general, you just replace x and y with their expressions in terms of r and theta (were you taught those?), and then do whatever is needed (in this case, solve for r).

Please show us whatever you have done; if you can't do anything, show us what you were taught about polar coordinates, such as the equations for x and y. If you have no source, this would be a good place to start: Paul's Online Math Notes.
 
re:

I figured out the first one.

For x^2(x^2+y^2)=7y^2, here's what I'm doing:

x^2(r^2)=7y^2

(rcost)^2(r^2)=7(rsint)^2

r^2=[7(rsint)^2]/(rcost)^2

r=sqrt(7tant^2)

I'm not sure where I'm going wrong. FYI, I'm entering the answer into Webwork, which is sometimes picky about the form of the answer.
 
13whispers said:
I figured out the first one.

For x^2(x^2+y^2)=7y^2, here's what I'm doing:

x^2(r^2)=7y^2

(rcost)^2(r^2)=7(rsint)^2

r^2=[7(rsint)^2]/(rcost)^2

r=sqrt(7tant^2)

I'm not sure where I'm going wrong. FYI, I'm entering the answer into Webwork, which is sometimes picky about the form of the answer.
Click to expand...

If you typed it in just as you show here, it would definitely be unhappy.

Assuming you are supposed to use t in place of theta, your last line should look like this, where I am being careful to show what is being squared:

r = sqrt(7 (tan(t))^2)

It is not t, but its tangent, that is squared. (Traditionally, we would write this part as tan^2 t, but a computer likely would not allow that.)

You could further simplify this, by breaking up the radical; that may or may not be demanded. Note that since you are told to assume that r>0, you can simplify the root of a square without worrying about signs.

If it still doesn't take your answer after fixing these two things, tell me exactly what you typed in, maybe even with a screen shot. Apart from these issues, your work looks good.
 
Dr.Peterson said:
If you typed it in just as you show here, it would definitely be unhappy.

Assuming you are supposed to use t in place of theta, your last line should look like this, where I am being careful to show what is being squared:

r = sqrt(7 (tan(t))^2)

It is not t, but its tangent, that is squared. (Traditionally, we would write this part as tan^2 t, but a computer likely would not allow that.)

You could further simplify this, by breaking up the radical; that may or may not be demanded. Note that since you are told to assume that r>0, you can simplify the root of a square without worrying about signs.

If it still doesn't take your answer after fixing these two things, tell me exactly what you typed in, maybe even with a screen shot. Apart from these issues, your work looks good.
Click to expand...

It wanted the simplified version, r=sqrt(7)tan(t).

Thank you!
 
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