Re: A-Level Simultaneous Equation Question


"Guess who" <notreally.here@xxxxxxxx> wrote in message
news:btlo22dls7s07v226ri8os10i54kukh12k@xxxxxxxxxx
On Thu, 30 Mar 2006 16:35:34 GMT, "Brian Reay" <see@xxxxxxxxxxxxxxx>
wrote:

Just to add to Andy's thoughts, do a sketch (or better still use a package
like Autograph) of the non-linear equation and, decide where the line must
lay to touch the curve just once (is isn't clear if your line is y=2x+k
or
y-2x+k =0 but, either way, there is enough to give you lines to explore.

Then, having visualised the situation, I think you could do it. You sketch
should give you a feel for the values of k that you seek.

Yes, but that only indicates an empirical result of somewhere about
+-8. The diagram doesn't lead to the actual solution, +-sqrt(65), but
the algebra does. Substitution, then knowledge of condition for
tangency will make the discriminant zero. It relies then more on
background studies in algebra, I think, rather than what the diagram
reveals. Certainly a diagram shows that there will be a family of
lines, some of which will cross the ellipse, and two of which will be
tangent, but does little towards the actua method of solution.


It seemed the original question indicated that the student had the
essentials of the method- ie simult. equation approach- but lacked an grasp
of the relationship of the lines to the ellipse. Andy indicated the tangent
condition but, in my view, that could be augmented by the use of a diagram
to steer the student toward seeing not only this problem but also a
technique for others.

As regards finding the answer, the sketch would give feel for the values of
k that could be expected- useful to give the student some confidence when he
gets his solutions.

Whether you like the use of a diagram all depends if your aim in teaching
includes developing the students problem solving and thinking skills or just
leading them to the answer. I prefer the former.

--
73
Brian
www.g8osn.org.uk







.

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