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Is $r^2-4rcos(theta)=14$ an equation of a circle or cylinder?


Is $r=2cos(theta)$ a one-petal polar function?General Cartesian/Rectangular Equation for Polar Rose ($r=sin(ktheta)$)Calculate Area of SurfaceSketch $r=cos(5 theta)$? $r$ as a function of $theta$ in cartesian coordinatesTo prove $(sintheta + csctheta)^2 + (costheta +sectheta)^2 ge 9$How to convert $r = 2scos (theta+t)$ into Cartesian coordinates?How can this be the surface area of an intersection of cone and cylinder?Question on polar coordinates and cartesian coordinatesHow to sketch $lnleft(sqrtx^2+y^2right)=-arctanleft(fracyxright)$ in polar coordinates?Show that $ sqrt2 + sqrt2 + sqrt2 + 2 cos 8theta = 2 cos theta$













0












$begingroup$


A question asks to identify the surface of the polar equation
beginequationtag1
r^2-4rcos(theta)=14.
endequation

I converted $(1)$ into Cartesian coordinates:
beginequationtag2
(x-2)^2+y^2 = (3sqrt2)^2.
endequation

I would have thought $(2)$ represents the equation of a cylinder, because the question asks to identify a surface.










share|cite|improve this question









$endgroup$











  • $begingroup$
    in how many dimensions?
    $endgroup$
    – J. W. Tanner
    Mar 14 at 16:07






  • 1




    $begingroup$
    In $mathbbR^2$ it's a circle. In $mathbbR^3$ it's a cylinder (using cylindrical coordinates $(x,y,z)=(rcostheta,rsintheta,z)$).
    $endgroup$
    – Barry Cipra
    Mar 14 at 16:08











  • $begingroup$
    @BarryCipra Okay. So is the answer dependent on the context of the question?
    $endgroup$
    – Gurjinder
    Mar 14 at 16:11










  • $begingroup$
    @Gurjinder, yes, exactly.
    $endgroup$
    – Barry Cipra
    Mar 14 at 16:12










  • $begingroup$
    @BarryCipra Cool, thanks.
    $endgroup$
    – Gurjinder
    Mar 14 at 16:13















0












$begingroup$


A question asks to identify the surface of the polar equation
beginequationtag1
r^2-4rcos(theta)=14.
endequation

I converted $(1)$ into Cartesian coordinates:
beginequationtag2
(x-2)^2+y^2 = (3sqrt2)^2.
endequation

I would have thought $(2)$ represents the equation of a cylinder, because the question asks to identify a surface.










share|cite|improve this question









$endgroup$











  • $begingroup$
    in how many dimensions?
    $endgroup$
    – J. W. Tanner
    Mar 14 at 16:07






  • 1




    $begingroup$
    In $mathbbR^2$ it's a circle. In $mathbbR^3$ it's a cylinder (using cylindrical coordinates $(x,y,z)=(rcostheta,rsintheta,z)$).
    $endgroup$
    – Barry Cipra
    Mar 14 at 16:08











  • $begingroup$
    @BarryCipra Okay. So is the answer dependent on the context of the question?
    $endgroup$
    – Gurjinder
    Mar 14 at 16:11










  • $begingroup$
    @Gurjinder, yes, exactly.
    $endgroup$
    – Barry Cipra
    Mar 14 at 16:12










  • $begingroup$
    @BarryCipra Cool, thanks.
    $endgroup$
    – Gurjinder
    Mar 14 at 16:13













0












0








0


1



$begingroup$


A question asks to identify the surface of the polar equation
beginequationtag1
r^2-4rcos(theta)=14.
endequation

I converted $(1)$ into Cartesian coordinates:
beginequationtag2
(x-2)^2+y^2 = (3sqrt2)^2.
endequation

I would have thought $(2)$ represents the equation of a cylinder, because the question asks to identify a surface.










share|cite|improve this question









$endgroup$




A question asks to identify the surface of the polar equation
beginequationtag1
r^2-4rcos(theta)=14.
endequation

I converted $(1)$ into Cartesian coordinates:
beginequationtag2
(x-2)^2+y^2 = (3sqrt2)^2.
endequation

I would have thought $(2)$ represents the equation of a cylinder, because the question asks to identify a surface.







algebra-precalculus graphing-functions surfaces






share|cite|improve this question













share|cite|improve this question











share|cite|improve this question




share|cite|improve this question










asked Mar 14 at 16:02









GurjinderGurjinder

552417




552417











  • $begingroup$
    in how many dimensions?
    $endgroup$
    – J. W. Tanner
    Mar 14 at 16:07






  • 1




    $begingroup$
    In $mathbbR^2$ it's a circle. In $mathbbR^3$ it's a cylinder (using cylindrical coordinates $(x,y,z)=(rcostheta,rsintheta,z)$).
    $endgroup$
    – Barry Cipra
    Mar 14 at 16:08











  • $begingroup$
    @BarryCipra Okay. So is the answer dependent on the context of the question?
    $endgroup$
    – Gurjinder
    Mar 14 at 16:11










  • $begingroup$
    @Gurjinder, yes, exactly.
    $endgroup$
    – Barry Cipra
    Mar 14 at 16:12










  • $begingroup$
    @BarryCipra Cool, thanks.
    $endgroup$
    – Gurjinder
    Mar 14 at 16:13
















  • $begingroup$
    in how many dimensions?
    $endgroup$
    – J. W. Tanner
    Mar 14 at 16:07






  • 1




    $begingroup$
    In $mathbbR^2$ it's a circle. In $mathbbR^3$ it's a cylinder (using cylindrical coordinates $(x,y,z)=(rcostheta,rsintheta,z)$).
    $endgroup$
    – Barry Cipra
    Mar 14 at 16:08











  • $begingroup$
    @BarryCipra Okay. So is the answer dependent on the context of the question?
    $endgroup$
    – Gurjinder
    Mar 14 at 16:11










  • $begingroup$
    @Gurjinder, yes, exactly.
    $endgroup$
    – Barry Cipra
    Mar 14 at 16:12










  • $begingroup$
    @BarryCipra Cool, thanks.
    $endgroup$
    – Gurjinder
    Mar 14 at 16:13















$begingroup$
in how many dimensions?
$endgroup$
– J. W. Tanner
Mar 14 at 16:07




$begingroup$
in how many dimensions?
$endgroup$
– J. W. Tanner
Mar 14 at 16:07




1




1




$begingroup$
In $mathbbR^2$ it's a circle. In $mathbbR^3$ it's a cylinder (using cylindrical coordinates $(x,y,z)=(rcostheta,rsintheta,z)$).
$endgroup$
– Barry Cipra
Mar 14 at 16:08





$begingroup$
In $mathbbR^2$ it's a circle. In $mathbbR^3$ it's a cylinder (using cylindrical coordinates $(x,y,z)=(rcostheta,rsintheta,z)$).
$endgroup$
– Barry Cipra
Mar 14 at 16:08













$begingroup$
@BarryCipra Okay. So is the answer dependent on the context of the question?
$endgroup$
– Gurjinder
Mar 14 at 16:11




$begingroup$
@BarryCipra Okay. So is the answer dependent on the context of the question?
$endgroup$
– Gurjinder
Mar 14 at 16:11












$begingroup$
@Gurjinder, yes, exactly.
$endgroup$
– Barry Cipra
Mar 14 at 16:12




$begingroup$
@Gurjinder, yes, exactly.
$endgroup$
– Barry Cipra
Mar 14 at 16:12












$begingroup$
@BarryCipra Cool, thanks.
$endgroup$
– Gurjinder
Mar 14 at 16:13




$begingroup$
@BarryCipra Cool, thanks.
$endgroup$
– Gurjinder
Mar 14 at 16:13










2 Answers
2






active

oldest

votes


















0












$begingroup$

This is of course a circle. General formula for the circle is $$(x-p)^2+(y-q)^2 =r^2$$



where $O=(p,q)$ is a center and $r$ radius. At your case $O=(2,0)$ and $r=3sqrt2$






share|cite|improve this answer









$endgroup$








  • 2




    $begingroup$
    I think we should recognize that this is also the equation of a cylinder whose axis of symmetry is parallel to the $z$ axis
    $endgroup$
    – WW1
    Mar 14 at 16:08


















0












$begingroup$

$$beginequationtag1
r^2-4rcos(theta)=14.
endequation$$

$$x^2+y^2-4x=14$$
$$(x-2)^2+y^2=18$$
$$(x-2)^2+y^2=(3sqrt2)^2$$






share|cite|improve this answer









$endgroup$












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    2 Answers
    2






    active

    oldest

    votes








    2 Answers
    2






    active

    oldest

    votes









    active

    oldest

    votes






    active

    oldest

    votes









    0












    $begingroup$

    This is of course a circle. General formula for the circle is $$(x-p)^2+(y-q)^2 =r^2$$



    where $O=(p,q)$ is a center and $r$ radius. At your case $O=(2,0)$ and $r=3sqrt2$






    share|cite|improve this answer









    $endgroup$








    • 2




      $begingroup$
      I think we should recognize that this is also the equation of a cylinder whose axis of symmetry is parallel to the $z$ axis
      $endgroup$
      – WW1
      Mar 14 at 16:08















    0












    $begingroup$

    This is of course a circle. General formula for the circle is $$(x-p)^2+(y-q)^2 =r^2$$



    where $O=(p,q)$ is a center and $r$ radius. At your case $O=(2,0)$ and $r=3sqrt2$






    share|cite|improve this answer









    $endgroup$








    • 2




      $begingroup$
      I think we should recognize that this is also the equation of a cylinder whose axis of symmetry is parallel to the $z$ axis
      $endgroup$
      – WW1
      Mar 14 at 16:08













    0












    0








    0





    $begingroup$

    This is of course a circle. General formula for the circle is $$(x-p)^2+(y-q)^2 =r^2$$



    where $O=(p,q)$ is a center and $r$ radius. At your case $O=(2,0)$ and $r=3sqrt2$






    share|cite|improve this answer









    $endgroup$



    This is of course a circle. General formula for the circle is $$(x-p)^2+(y-q)^2 =r^2$$



    where $O=(p,q)$ is a center and $r$ radius. At your case $O=(2,0)$ and $r=3sqrt2$







    share|cite|improve this answer












    share|cite|improve this answer



    share|cite|improve this answer










    answered Mar 14 at 16:05









    Maria MazurMaria Mazur

    47.9k1260120




    47.9k1260120







    • 2




      $begingroup$
      I think we should recognize that this is also the equation of a cylinder whose axis of symmetry is parallel to the $z$ axis
      $endgroup$
      – WW1
      Mar 14 at 16:08












    • 2




      $begingroup$
      I think we should recognize that this is also the equation of a cylinder whose axis of symmetry is parallel to the $z$ axis
      $endgroup$
      – WW1
      Mar 14 at 16:08







    2




    2




    $begingroup$
    I think we should recognize that this is also the equation of a cylinder whose axis of symmetry is parallel to the $z$ axis
    $endgroup$
    – WW1
    Mar 14 at 16:08




    $begingroup$
    I think we should recognize that this is also the equation of a cylinder whose axis of symmetry is parallel to the $z$ axis
    $endgroup$
    – WW1
    Mar 14 at 16:08











    0












    $begingroup$

    $$beginequationtag1
    r^2-4rcos(theta)=14.
    endequation$$

    $$x^2+y^2-4x=14$$
    $$(x-2)^2+y^2=18$$
    $$(x-2)^2+y^2=(3sqrt2)^2$$






    share|cite|improve this answer









    $endgroup$

















      0












      $begingroup$

      $$beginequationtag1
      r^2-4rcos(theta)=14.
      endequation$$

      $$x^2+y^2-4x=14$$
      $$(x-2)^2+y^2=18$$
      $$(x-2)^2+y^2=(3sqrt2)^2$$






      share|cite|improve this answer









      $endgroup$















        0












        0








        0





        $begingroup$

        $$beginequationtag1
        r^2-4rcos(theta)=14.
        endequation$$

        $$x^2+y^2-4x=14$$
        $$(x-2)^2+y^2=18$$
        $$(x-2)^2+y^2=(3sqrt2)^2$$






        share|cite|improve this answer









        $endgroup$



        $$beginequationtag1
        r^2-4rcos(theta)=14.
        endequation$$

        $$x^2+y^2-4x=14$$
        $$(x-2)^2+y^2=18$$
        $$(x-2)^2+y^2=(3sqrt2)^2$$







        share|cite|improve this answer












        share|cite|improve this answer



        share|cite|improve this answer










        answered Mar 14 at 16:09









        E.H.EE.H.E

        15.9k11968




        15.9k11968



























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