Search results

Thanks Spice. Also thought along those lines but decided it was too fiddly. Hope we are not driving the students too quickly towards question 8. How were you at this time last year? Don't tell me -you've been seeking out q7/8's since Yr.11! Care to help ND out on the Ellipse question?

Yes.

Sorrry, I meant S', P and S".

ND: part (ii). Hope you have drawn an ellipse, a tangent line, the two foci, and equal inclinations of the focal chords. Can you show that S", P and S are collinear?

ND : unfortunately, because of the +positive-negative ie. x^2/a^2-y^2/b^2 of the hyperbola, the p,q inequality is useless- the reason for using the discriminant instead. However, I'll be interested in an alternative to the discriminant for this question.

Here's the hyperbola morph of the ellipse question 8, 1995. a)Consider the line y=mx+c and the hyperbola H, x^2/a^2-y^2/b^2=1. Show that the conditions for cutting, touching and avoiding are c^2>(am)^2-b^2, c^2=(am)^2-b^2, and c^2<(am)^2-b^2 respectively. b)The point M(X_0,Y_0) lies...

Had problems logging into the site. I also beg your pardon, thought this "length of intercept property" generalized as did the "area of triangle property", got my atan and bsec crossed, I guess we can't nail Geha twice. assume s=sec@, t=tan@ OP^2=(as)^2 + (bt)^2...

ND: you had me worried, so I rechecked my calculations. The area of hyperbola triangle question was also morphed out of Geha's who assumes the easier rectangular hyperbola case "area of triangle property"; that's why I became suspicious of this "length of intercept property", whether it could...

ND : good thoughtful questions. For part i) you can say that no loss of generality in assuming the ellipse x^2/a^2+y^2/b^2=1. For part ii) I specifically avoided the word "locus" as the only derivation of a locus eqn. required in the syllabus is with the rectangular hyperbola. A description...

P is an arbitrary pt. on the ellipse and line L is the tangent to the ellipse at P. The pts. S' and S are the foci of the ellipse. Let S" be the reflection of S across the L. i) Prove that the focal chords through P are equally inclined. ii) Fully describe the path of S" as P moves on the...

The tangent at P(asec@,btan@) on a hyperbola meets the asymptotes at QR. Show that QR is twice the distance of the chord joining point P with the intersection of the asymptotes. Note: this question is a morph of Geha's question for the special rectangular hyperbola case ie. P(cp,c/p).

Underthesun :"and, it seems that my way requires using the distance formula.." Not all is lost, I am posting another Hyperbola problem in a new thread using the distance formula.

The question was not posted like an exam question. If this q was in the exam, there would be a few leading questions- it is amazing how the examiner leads you by the hand. Perhaps part i) might be : show that eqn. of tangent is xsec@/a-ytan@/@=1; part ii) show equation of the asymptotes; part...

I meant go over the solution, find out what makes it elegant, and usually the structure of the solution will provide you pointers in how an examiner's mind works. eg. if this was shown for an ellipse, what is the corresponding hyperbola question, or if something is valid for n=5, can you answer...

Great. Splitting that triangle so as to have the same horizontal base is definitely elegant!

Yes you may. But to be sure, remind the examiner that since it's in the first quadrant sin2@>0.

Remember : one good song is better than 100 lousy songs.

Prove that the area of the triangle formed by the tangent to the hyperbola and the asymptotes is a constant.

ND : Nice. A few months back you were asking how you might increase your Elegance Quotient. Elegant answers beget elegant questions and so on. In this forum for example, problems have been posed and elegant solutions (particularly Spice Girl's) presented. Look at an elegant solution and see...

You are right.