Recent content by Appleton

Thanks for your reply Mark44. Sorry for my delay. Is your interpretation of 2 lines "equally inclined to the axes of coordinates" equivalent to saying that the lines are perpendicular?

Homework Statement Prove that the chord joining the points P(cp, c/p) and Q(cq, c/q) on the rectangular hyperbola xy = c^2 has the equation x + pqy = c(p + q) The points P, Q, R are given on the rectangular hyperbola xy = c^2 . prove that (a) if PQ and PR are equally inclined to the axes of...

OK I think I'm with you now. Thanks for the prompt. I think the implicit derivative was my main stumbling block, amongst various other oversights.

Thanks for your reply micromass. I realize I made a mistake. P(p,q) does not lie on the conic. The polar is the chord of contact of the tangents from P. If the point lies on the conic then the chord of contact would be non existent as P and the tangent points would all be coincident. If we...

If a general conic is ax^2+2hxy+by^2+2gx+2fy+c=0 I am told that, if P(p, q) is a point on this conic, then the polar of P(p, q) to this conic is apx+h(py+qx)+bgy+g(p+x)+f(q+y)+c=0 How is this derived?

That seems to have done the trick. So the point of intersection is the constant value a(\frac{a^2+b^2}{a^2-b^2},0) Thanks for your help.

Homework Statement Show that the equation of the chord joining the points P(a\cos(\phi), b\sin(\phi)) and Q(a\cos(\theta), b\sin(\theta)) on the ellipse b^2x^2+a^2y^2=a^2b^2 is bx cos\frac{1}{2}(\theta+\phi)+ay\sin\frac{1}{2}(\theta+\phi)=ab\cos\frac{1}{2}(\theta-\phi). Prove that , if the...

Thanks for that, it makes sense now, so the asymptotes must be y =+-x

Thanks for your reply andrewkirk. Unfortunately I'm still not able to identify my error. Here are the steps I omitted: AP.PA' = ((a-x)\boldsymbol i + y\boldsymbol j).((-a-x)\boldsymbol i+y\boldsymbol j) The dot product is distributive over vector addition, so AP.PA' = (a-x)\boldsymbol...

Homework Statement A point P moves so that its distances from A(a, 0), A'(-a, 0), B(b, 0) B'(-b, 0) are related by the equation AP.PA'=BP.PB'. Show that the locus of P is a hyperbola and find the equations of its asymptotes. Homework EquationsThe Attempt at a Solution AP.PA' =...

Hi, I'm hoping no news is good news. It's the last part of the question that I'm most curious about. Is my book correct? Or am I correct? Or neither?

Homework Statement [/B] The tangent and the normal at a point P(3\sqrt2\cos\theta,3\sin\theta)) on the ellipse \frac{x^2}{18}+\frac{y^2}{9}=1 meet the y-axis at T and N respectively. If O is the origin, prove that OT.TN is independent of the position P. Find the coordinates of X, the centre of...

The chapter of the book is called coordinate geometry. I'm not sure if there is a more appropriate title for this branch of maths.

Looks like the negative square root i produced above was an error. Having gone through it again I am able to produce the values for c in the question. Thank you for identifying my error in mixing up a and b.

Isn't the convention to assign a to the value of the semi major axis? In this case 35/3 > 35/8 so shouldn't a=35/3 and b=35/8? To check I'm not mistaken I repeated the procedure above, swapping a and b, and ended up with the square root of a negative number.