Loading ...
Sorry, an error occurred while loading the content.
 

Re: Conics

Expand Messages
  • cs_smile
    yeah ^_^||| coz i havta prep for public exam, argh... anyway, glad that u remember me and is still around w/ slim. btw, i havta wear mask during all my
    Message 1 of 7 , Apr 30, 2003
      yeah ^_^||| coz i havta prep for public exam, argh...

      anyway, glad that u remember me and is still around w/ slim.

      btw, i havta wear mask during all my examinations! becoz of the
      atypical pneumonia! well, i live in Hong Kong, and that's quite self-
      explanatory... >_< im always trapped at home!

      --- In mathforfun@yahoogroups.com, clooneman <no_reply@y...> wrote:
      > You've not been around for ages, have you?
      >
      > --- In mathforfun@yahoogroups.com, cs_smile <no_reply@y...> wrote:
      > > can anybody help me out? i am desperate, coz im gonna have my
      open
      > > exam next week. I would be grateful if anyone can help!
      > > Thx!
      > >
      > > --- In mathforfun@yahoogroups.com, cs_smile <no_reply@y...> wrote:
      > > > pls help!
      > > >
      > > > here's the problem:
      > > >
      > > > note: pls refer to the photos>problems> conics1 and conics 2
      pics
      > > > for the diagrams.
      > > >
      > > > (a) Figure 6(a) shows three straight lines L1:y=k, L2 which has
      a
      > > > slpe m and L, all of them pass through the point (h,k) and L2
      is
      > > the
      > > > angle bisector of L and L1.
      > > >
      > > > (1) Let @ and (@2) be the inclinations of L and L2
      > > > respectively. Show that @=2(@2)-180.
      > > > (2) Hence, or otherwise, find the equation of L, in
      terms of
      > > > h, k and m.
      > > >
      > > > (b) (1) Figure 6(b) shows part of a circle C: x^2+y^2=r^2,
      where
      > r
      > > > is a positive constant. P(r cos @, r sin @) is a point on C. L3
      > > and
      > > > L4 are straight lines passing through P with L3 parallel to the
      x-
      > > > axis.
      > > > (i) Find the slope, in terms of @, of the normal to C
      at P.
      > > > (ii) Using (a), or otherwise, find the equation of L4 in
      terms
      > > > of @.
      > > >
      > > > (2) Figure 6(c) shows a parabola S: y^2=4ax, where a is
      a
      > > > positive constant. Q(at^2, 2at) is a point on S. L5 and L6 are
      > > > straight lines passing through Q with L5 parallel to the x-axis.
      > > > (i) Find the slope, in terms of @, of the normal to S
      at Q.
      > > > (ii) Find the equation of L6 in terms of t.
      > > >
      > > > (c) A student wants to use a curve mirror to focus a parallel
      > > light
      > > > beam to a fixed point. Explain whether he should use a circular
      > > > mirror or a parabolic mirror.
      > > >
      > > >
      > > > thx!
    • clooneman
      Is it true that people there can t handle the claustrophobia of confinement and have tried to jump out windows? ... self- ... has ... L3 ... the ... in ... is
      Message 2 of 7 , May 1, 2003
        Is it true that people there can't handle the claustrophobia of
        confinement and have tried to jump out windows?

        --- In mathforfun@yahoogroups.com, cs_smile <no_reply@y...> wrote:
        > yeah ^_^||| coz i havta prep for public exam, argh...
        >
        > anyway, glad that u remember me and is still around w/ slim.
        >
        > btw, i havta wear mask during all my examinations! becoz of the
        > atypical pneumonia! well, i live in Hong Kong, and that's quite
        self-
        > explanatory... >_< im always trapped at home!
        >
        > --- In mathforfun@yahoogroups.com, clooneman <no_reply@y...> wrote:
        > > You've not been around for ages, have you?
        > >
        > > --- In mathforfun@yahoogroups.com, cs_smile <no_reply@y...> wrote:
        > > > can anybody help me out? i am desperate, coz im gonna have my
        > open
        > > > exam next week. I would be grateful if anyone can help!
        > > > Thx!
        > > >
        > > > --- In mathforfun@yahoogroups.com, cs_smile <no_reply@y...>
        wrote:
        > > > > pls help!
        > > > >
        > > > > here's the problem:
        > > > >
        > > > > note: pls refer to the photos>problems> conics1 and conics 2
        > pics
        > > > > for the diagrams.
        > > > >
        > > > > (a) Figure 6(a) shows three straight lines L1:y=k, L2 which
        has
        > a
        > > > > slpe m and L, all of them pass through the point (h,k) and L2
        > is
        > > > the
        > > > > angle bisector of L and L1.
        > > > >
        > > > > (1) Let @ and (@2) be the inclinations of L and L2
        > > > > respectively. Show that @=2(@2)-180.
        > > > > (2) Hence, or otherwise, find the equation of L, in
        > terms of
        > > > > h, k and m.
        > > > >
        > > > > (b) (1) Figure 6(b) shows part of a circle C: x^2+y^2=r^2,
        > where
        > > r
        > > > > is a positive constant. P(r cos @, r sin @) is a point on C.
        L3
        > > > and
        > > > > L4 are straight lines passing through P with L3 parallel to
        the
        > x-
        > > > > axis.
        > > > > (i) Find the slope, in terms of @, of the normal to C
        > at P.
        > > > > (ii) Using (a), or otherwise, find the equation of L4
        in
        > terms
        > > > > of @.
        > > > >
        > > > > (2) Figure 6(c) shows a parabola S: y^2=4ax, where a
        is
        > a
        > > > > positive constant. Q(at^2, 2at) is a point on S. L5 and L6
        are
        > > > > straight lines passing through Q with L5 parallel to the x-
        axis.
        > > > > (i) Find the slope, in terms of @, of the normal to S
        > at Q.
        > > > > (ii) Find the equation of L6 in terms of t.
        > > > >
        > > > > (c) A student wants to use a curve mirror to focus a parallel
        > > > light
        > > > > beam to a fixed point. Explain whether he should use a
        circular
        > > > > mirror or a parabolic mirror.
        > > > >
        > > > >
        > > > > thx!
      • cs_smile
        Nope, that is Taiwan. HK medical stuff is more responsible and will never jump out juz to escape. they stay and help the patients to fight the disease... and
        Message 3 of 7 , May 2, 2003
          Nope, that is Taiwan. HK medical stuff is more responsible and will
          never jump out juz to escape. they stay and help the patients to
          fight the disease... and risking their lifes...

          anyway, do u mind helping me out with this conics problem? im stuck
          at finding the equations of the lines after find their slopes. i
          cant apply the result in part (a).

          --- In mathforfun@yahoogroups.com, clooneman <no_reply@y...> wrote:
          > Is it true that people there can't handle the claustrophobia of
          > confinement and have tried to jump out windows?
          >
          > --- In mathforfun@yahoogroups.com, cs_smile <no_reply@y...> wrote:
          > > yeah ^_^||| coz i havta prep for public exam, argh...
          > >
          > > anyway, glad that u remember me and is still around w/ slim.
          > >
          > > btw, i havta wear mask during all my examinations! becoz of the
          > > atypical pneumonia! well, i live in Hong Kong, and that's quite
          > self-
          > > explanatory... >_< im always trapped at home!
          > >
          > > --- In mathforfun@yahoogroups.com, clooneman <no_reply@y...>
          wrote:
          > > > You've not been around for ages, have you?
          > > >
          > > > --- In mathforfun@yahoogroups.com, cs_smile <no_reply@y...>
          wrote:
          > > > > can anybody help me out? i am desperate, coz im gonna have
          my
          > > open
          > > > > exam next week. I would be grateful if anyone can help!
          > > > > Thx!
          > > > >
          > > > > --- In mathforfun@yahoogroups.com, cs_smile <no_reply@y...>
          > wrote:
          > > > > > pls help!
          > > > > >
          > > > > > here's the problem:
          > > > > >
          > > > > > note: pls refer to the photos>problems> conics1 and conics
          2
          > > pics
          > > > > > for the diagrams.
          > > > > >
          > > > > > (a) Figure 6(a) shows three straight lines L1:y=k, L2
          which
          > has
          > > a
          > > > > > slpe m and L, all of them pass through the point (h,k) and
          L2
          > > is
          > > > > the
          > > > > > angle bisector of L and L1.
          > > > > >
          > > > > > (1) Let @ and (@2) be the inclinations of L and L2
          > > > > > respectively. Show that @=2(@2)-180.
          > > > > > (2) Hence, or otherwise, find the equation of L, in
          > > terms of
          > > > > > h, k and m.
          > > > > >
          > > > > > (b) (1) Figure 6(b) shows part of a circle C: x^2+y^2=r^2,
          > > where
          > > > r
          > > > > > is a positive constant. P(r cos @, r sin @) is a point on
          C.
          > L3
          > > > > and
          > > > > > L4 are straight lines passing through P with L3 parallel
          to
          > the
          > > x-
          > > > > > axis.
          > > > > > (i) Find the slope, in terms of @, of the normal to C
          > > at P.
          > > > > > (ii) Using (a), or otherwise, find the equation of L4
          > in
          > > terms
          > > > > > of @.
          > > > > >
          > > > > > (2) Figure 6(c) shows a parabola S: y^2=4ax, where a
          > is
          > > a
          > > > > > positive constant. Q(at^2, 2at) is a point on S. L5 and L6
          > are
          > > > > > straight lines passing through Q with L5 parallel to the x-
          > axis.
          > > > > > (i) Find the slope, in terms of @, of the normal to S
          > > at Q.
          > > > > > (ii) Find the equation of L6 in terms of t.
          > > > > >
          > > > > > (c) A student wants to use a curve mirror to focus a
          parallel
          > > > > light
          > > > > > beam to a fixed point. Explain whether he should use a
          > circular
          > > > > > mirror or a parabolic mirror.
          > > > > >
          > > > > >
          > > > > > thx!
        • cs_smile
          Nope, that is Taiwan. HK medical stuff is more responsible and will never jump out juz to escape. they stay and help the patients to fight the disease... and
          Message 4 of 7 , May 2, 2003
            Nope, that is Taiwan. HK medical stuff is more responsible and will
            never jump out juz to escape. they stay and help the patients to
            fight the disease... and risking their lifes...

            anyway, do u mind helping me out with this conics problem? im stuck
            at finding the equations of the lines after find their slopes. i
            cant apply the result in part (a).

            --- In mathforfun@yahoogroups.com, clooneman <no_reply@y...> wrote:
            > Is it true that people there can't handle the claustrophobia of
            > confinement and have tried to jump out windows?
            >
            > --- In mathforfun@yahoogroups.com, cs_smile <no_reply@y...> wrote:
            > > yeah ^_^||| coz i havta prep for public exam, argh...
            > >
            > > anyway, glad that u remember me and is still around w/ slim.
            > >
            > > btw, i havta wear mask during all my examinations! becoz of the
            > > atypical pneumonia! well, i live in Hong Kong, and that's quite
            > self-
            > > explanatory... >_< im always trapped at home!
            > >
            > > --- In mathforfun@yahoogroups.com, clooneman <no_reply@y...>
            wrote:
            > > > You've not been around for ages, have you?
            > > >
            > > > --- In mathforfun@yahoogroups.com, cs_smile <no_reply@y...>
            wrote:
            > > > > can anybody help me out? i am desperate, coz im gonna have
            my
            > > open
            > > > > exam next week. I would be grateful if anyone can help!
            > > > > Thx!
            > > > >
            > > > > --- In mathforfun@yahoogroups.com, cs_smile <no_reply@y...>
            > wrote:
            > > > > > pls help!
            > > > > >
            > > > > > here's the problem:
            > > > > >
            > > > > > note: pls refer to the photos>problems> conics1 and conics
            2
            > > pics
            > > > > > for the diagrams.
            > > > > >
            > > > > > (a) Figure 6(a) shows three straight lines L1:y=k, L2
            which
            > has
            > > a
            > > > > > slpe m and L, all of them pass through the point (h,k) and
            L2
            > > is
            > > > > the
            > > > > > angle bisector of L and L1.
            > > > > >
            > > > > > (1) Let @ and (@2) be the inclinations of L and L2
            > > > > > respectively. Show that @=2(@2)-180.
            > > > > > (2) Hence, or otherwise, find the equation of L, in
            > > terms of
            > > > > > h, k and m.
            > > > > >
            > > > > > (b) (1) Figure 6(b) shows part of a circle C: x^2+y^2=r^2,
            > > where
            > > > r
            > > > > > is a positive constant. P(r cos @, r sin @) is a point on
            C.
            > L3
            > > > > and
            > > > > > L4 are straight lines passing through P with L3 parallel
            to
            > the
            > > x-
            > > > > > axis.
            > > > > > (i) Find the slope, in terms of @, of the normal to C
            > > at P.
            > > > > > (ii) Using (a), or otherwise, find the equation of L4
            > in
            > > terms
            > > > > > of @.
            > > > > >
            > > > > > (2) Figure 6(c) shows a parabola S: y^2=4ax, where a
            > is
            > > a
            > > > > > positive constant. Q(at^2, 2at) is a point on S. L5 and L6
            > are
            > > > > > straight lines passing through Q with L5 parallel to the x-
            > axis.
            > > > > > (i) Find the slope, in terms of @, of the normal to S
            > > at Q.
            > > > > > (ii) Find the equation of L6 in terms of t.
            > > > > >
            > > > > > (c) A student wants to use a curve mirror to focus a
            parallel
            > > > > light
            > > > > > beam to a fixed point. Explain whether he should use a
            > circular
            > > > > > mirror or a parabolic mirror.
            > > > > >
            > > > > >
            > > > > > thx!
          Your message has been successfully submitted and would be delivered to recipients shortly.